Pub Date : 2025-01-23DOI: 10.1016/j.chaos.2025.116005
A. Pezzi, G. Deng, Y. Lvov, M. Lorenzo, M. Onorato
We examine a diatomic chain with a cubic anharmonic potential. Following the celebrated α-FPUT model, we refer to the present system as the diatomic α–FPUT model. By introducing new canonical variables, we diagonalize the harmonic part of the Hamiltonian, and, using these new variables, we analyze the nonlinear interactions between the acoustic and optical branches of the dispersion relation. In terms of the new canonical variables, dynamical equations exhibit quadratic nonlinearity, with the first resonant process being a three-wave interaction. We thoroughly investigate the dependence of these resonant interactions on the mass ratio and find that they occur when the mass ratio is less than 3. Note that in the standard α-FPUT chain, three-wave resonances do not occur. We find that these three-wave resonances in the α-diatomic chain are mostly isolated. Consequently, the resonant manifold consists of uncoupled triplets. Therefore, they do not contribute to thermalization, and we consider higher-order resonances. Over a longer time scale, four-wave resonances become significant. For this scenario, we apply the Wave Turbulence theory, deriving two coupled wave kinetic equations and the corresponding equilibrium solution.
{"title":"Multi-wave resonances in the diatomic [formula omitted]-FPUT system","authors":"A. Pezzi, G. Deng, Y. Lvov, M. Lorenzo, M. Onorato","doi":"10.1016/j.chaos.2025.116005","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116005","url":null,"abstract":"We examine a diatomic chain with a cubic anharmonic potential. Following the celebrated <mml:math altimg=\"si5.svg\" display=\"inline\"><mml:mi>α</mml:mi></mml:math>-FPUT model, we refer to the present system as the diatomic <mml:math altimg=\"si5.svg\" display=\"inline\"><mml:mi>α</mml:mi></mml:math>–FPUT model. By introducing new canonical variables, we diagonalize the harmonic part of the Hamiltonian, and, using these new variables, we analyze the nonlinear interactions between the acoustic and optical branches of the dispersion relation. In terms of the new canonical variables, dynamical equations exhibit quadratic nonlinearity, with the first resonant process being a three-wave interaction. We thoroughly investigate the dependence of these resonant interactions on the mass ratio and find that they occur when the mass ratio is less than 3. Note that in the standard <mml:math altimg=\"si5.svg\" display=\"inline\"><mml:mi>α</mml:mi></mml:math>-FPUT chain, three-wave resonances do not occur. We find that these three-wave resonances in the <mml:math altimg=\"si5.svg\" display=\"inline\"><mml:mi>α</mml:mi></mml:math>-diatomic chain are mostly isolated. Consequently, the resonant manifold consists of uncoupled triplets. Therefore, they do not contribute to thermalization, and we consider higher-order resonances. Over a longer time scale, four-wave resonances become significant. For this scenario, we apply the Wave Turbulence theory, deriving two coupled wave kinetic equations and the corresponding equilibrium solution.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"25 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1016/j.chaos.2025.116047
Qichen Wang, Yuhao Zhao
In engineering applications, complex structural forms can often be approximated by coupled beam systems, underscoring the critical importance of vibration control in these structures. Leveraging the advantages of distributed nonlinear energy sinks (NES) in structural vibration management, this study introduces a distributed coupling nonlinear energy sink (CNES) into thin beam systems (TBS) and investigates its efficacy in reducing vibrations. A mathematical model of TBS incorporating distributed CNES is developed, and the Galerkin truncation method (GTM) is utilized to analyze TBS vibration response under harmonic excitation, confirming model accuracy. The effects of core parameters within the distributed CNES on the vibration reduction performance of TBS are systematically analyzed. Furthermore, the influence of varying distribution quantities of the distributed CNES on vibration behavior is also investigated. Numerical simulations reveal that optimized parameters for distributed CNES significantly enhance the vibration reduction ratio of TBS. However, certain parameter values may induce unconventional vibrational phenomena. This study finds that adjusting the distribution density of NES can not only mitigate these unconventional vibrations but also substantially boost vibration reduction efficacy. Compared to single CNES, distributed CNES offers a robust solution for controlling nonlinear-induced unconventional vibrations, allowing for effective vibration suppression in TBS without altering their intrinsic vibration characteristics.
{"title":"Vibration reduction research of a thin beam system by employing distributed coupling nonlinear energy sinks","authors":"Qichen Wang, Yuhao Zhao","doi":"10.1016/j.chaos.2025.116047","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116047","url":null,"abstract":"In engineering applications, complex structural forms can often be approximated by coupled beam systems, underscoring the critical importance of vibration control in these structures. Leveraging the advantages of distributed nonlinear energy sinks (NES) in structural vibration management, this study introduces a distributed coupling nonlinear energy sink (CNES) into thin beam systems (TBS) and investigates its efficacy in reducing vibrations. A mathematical model of TBS incorporating distributed CNES is developed, and the Galerkin truncation method (GTM) is utilized to analyze TBS vibration response under harmonic excitation, confirming model accuracy. The effects of core parameters within the distributed CNES on the vibration reduction performance of TBS are systematically analyzed. Furthermore, the influence of varying distribution quantities of the distributed CNES on vibration behavior is also investigated. Numerical simulations reveal that optimized parameters for distributed CNES significantly enhance the vibration reduction ratio of TBS. However, certain parameter values may induce unconventional vibrational phenomena. This study finds that adjusting the distribution density of NES can not only mitigate these unconventional vibrations but also substantially boost vibration reduction efficacy. Compared to single CNES, distributed CNES offers a robust solution for controlling nonlinear-induced unconventional vibrations, allowing for effective vibration suppression in TBS without altering their intrinsic vibration characteristics.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"22 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1016/j.chaos.2025.115997
Jianping Wu
In this paper, a novel Riemann–Hilbert (RH) formulation-based reduction method is developed for an integrable reverse-space nonlocal Manakov equation. Firstly, the scattering-data constraints of the reverse-space nonlocal Manakov equation are shown to be difficult to determine via the traditional RH method. Secondly, to obtain the scattering-data constraints of the reverse-space nonlocal Manakov equation, the traditional RH method is extended to an improved version which we call a novel RH formulation-based reduction method. Specifically, utilizing the RH formulation-based reduction method, the scattering-data constraints of the reverse-space nonlocal Manakov equation are determined to guarantee the required nonlocal symmetry reduction of the two-component Ablowitz–Kaup–Newell–Segur (AKNS) system. Moreover, the scattering-data constraints of the reverse-space nonlocal Manakov equation are compared with those of the Manakov equation. Thirdly, N-soliton solutions of the reverse-space nonlocal Manakov equation are obtained by imposing the obtained scattering-data constraints in those of the two-component AKNS system. Furthermore, the applications of our novel RH formulation-based reduction method are confirmed by applying it to another integrable nonlocal Manakov equation of reverse-spacetime type. Moreover, the scattering-data constraints of the reverse-spacetime nonlocal Manakov equation are further compared with those of the reverse-space nonlocal Manakov equation and the Manakov equation, respectively. Additionally, the nonlinear soliton features of the reverse-space nonlocal Manakov equation and the reverse-spacetime nonlocal Manakov equation are analyzed and classified in detail, respectively, according to different spectral parameter selections.
本文提出了一种新的基于Riemann-Hilbert （RH）公式的可积逆空间非局部Manakov方程约简方法。首先，利用传统的RH方法难以确定逆空间非局部Manakov方程的散射数据约束；其次，为了获得逆空间非局部Manakov方程的散射数据约束，将传统的RH方法扩展为一种改进的基于新RH公式的约简方法。具体而言，利用基于RH公式的约简方法，确定了逆空间非局部Manakov方程的散射数据约束，以保证双组分ablowitz - kap - newwell - segur （AKNS）系统具有所需的非局部对称性约简。此外，还比较了逆空间非局部Manakov方程与Manakov方程的散射数据约束。第三，将得到的散射数据约束作用于双分量AKNS系统的散射数据约束，得到逆空间非局部Manakov方程的n孤子解。此外，将基于RH公式的新约简方法应用于另一个逆时空型可积非局部Manakov方程，验证了该方法的应用。此外，还将反时空非局部Manakov方程的散射数据约束与反空间非局部Manakov方程和Manakov方程的散射数据约束进行了比较。此外，根据不同的谱参数选择，对逆空间非局部Manakov方程和逆时空非局部Manakov方程的非线性孤子特征进行了详细的分析和分类。
{"title":"A novel Riemann–Hilbert formulation-based reduction method to an integrable reverse-space nonlocal Manakov equation and its applications","authors":"Jianping Wu","doi":"10.1016/j.chaos.2025.115997","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.115997","url":null,"abstract":"In this paper, a novel Riemann–Hilbert (RH) formulation-based reduction method is developed for an integrable reverse-space nonlocal Manakov equation. Firstly, the scattering-data constraints of the reverse-space nonlocal Manakov equation are shown to be difficult to determine via the traditional RH method. Secondly, to obtain the scattering-data constraints of the reverse-space nonlocal Manakov equation, the traditional RH method is extended to an improved version which we call a novel RH formulation-based reduction method. Specifically, utilizing the RH formulation-based reduction method, the scattering-data constraints of the reverse-space nonlocal Manakov equation are determined to guarantee the required nonlocal symmetry reduction of the two-component Ablowitz–Kaup–Newell–Segur (AKNS) system. Moreover, the scattering-data constraints of the reverse-space nonlocal Manakov equation are compared with those of the Manakov equation. Thirdly, <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mi>N</mml:mi></mml:math>-soliton solutions of the reverse-space nonlocal Manakov equation are obtained by imposing the obtained scattering-data constraints in those of the two-component AKNS system. Furthermore, the applications of our novel RH formulation-based reduction method are confirmed by applying it to another integrable nonlocal Manakov equation of reverse-spacetime type. Moreover, the scattering-data constraints of the reverse-spacetime nonlocal Manakov equation are further compared with those of the reverse-space nonlocal Manakov equation and the Manakov equation, respectively. Additionally, the nonlinear soliton features of the reverse-space nonlocal Manakov equation and the reverse-spacetime nonlocal Manakov equation are analyzed and classified in detail, respectively, according to different spectral parameter selections.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"12 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1016/j.chaos.2025.116019
Akhtar Munir, Muqaddar Abbas, Chunfang Wang
Nonreciprocal cavity magnonics combines magnetics and photonics to provide a versatile platform for studying nonlinear interactions and spin–orbit coupling in optical systems. We present a theoretical framework to amplify the photonic spin Hall effect (SHE) in a nonreciprocal cavity magnonics system with two microwave cavity modes and a single magnon mode. By tuning the coupling strengths between clockwise (CW) and counterclockwise (CCW) microwave modes and magnons, we achieve a high isolation rate I>50, indicating high nonreciprocity. Using the transfer matrix approach, we compute the reflection coefficients of transverse magnetic (TM) and transverse electric (TE) polarized light, demonstrating amplified photonic SHE via control of CW and CCW coupling rates. The nonlinear dynamics arising from asymmetric spin splitting and enhanced photon-magnon interactions exhibit intriguing effects such as dynamic spin–orbit coupling, paving the way for advanced spin photonic devices. This study highlights the potential of cavity magnomechanics to extend the understanding of nonreciprocal phenomena and provides a pathway to developing spin-based photonic circuits, optical isolators, and polarization-sensitive devices for nonlinear optical applications.
{"title":"Nonreciprocal cavity magnonics system for amplification of photonic spin Hall effect","authors":"Akhtar Munir, Muqaddar Abbas, Chunfang Wang","doi":"10.1016/j.chaos.2025.116019","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116019","url":null,"abstract":"Nonreciprocal cavity magnonics combines magnetics and photonics to provide a versatile platform for studying nonlinear interactions and spin–orbit coupling in optical systems. We present a theoretical framework to amplify the photonic spin Hall effect (SHE) in a nonreciprocal cavity magnonics system with two microwave cavity modes and a single magnon mode. By tuning the coupling strengths between clockwise (CW) and counterclockwise (CCW) microwave modes and magnons, we achieve a high isolation rate <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:mi mathvariant=\"script\">I</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">></mml:mo><mml:mn>50</mml:mn></mml:mrow></mml:math>, indicating high nonreciprocity. Using the transfer matrix approach, we compute the reflection coefficients of transverse magnetic (TM) and transverse electric (TE) polarized light, demonstrating amplified photonic SHE via control of CW and CCW coupling rates. The nonlinear dynamics arising from asymmetric spin splitting and enhanced photon-magnon interactions exhibit intriguing effects such as dynamic spin–orbit coupling, paving the way for advanced spin photonic devices. This study highlights the potential of cavity magnomechanics to extend the understanding of nonreciprocal phenomena and provides a pathway to developing spin-based photonic circuits, optical isolators, and polarization-sensitive devices for nonlinear optical applications.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"51 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1016/j.chaos.2025.116007
Anil Radhakrishnan, Sudeshna Sinha, K. Murali, William L. Ditto
We present a method for configuring Chaogates to replicate standard Boolean logic gate behavior using gradient-based optimization. By defining a differentiable formulation of the Chaogate encoding, we optimize its tunable parameters to reconfigure the Chaogate for standard logic gate functions. This novel approach allows us to bring the well established tools of machine learning to optimizing Chaogates without the cost of high parameter count neural networks. We further extend this approach to the simultaneous optimization of multiple gates for tuning logic circuits. Experimental results demonstrate the viability of this technique across different nonlinear systems and configurations, offering a pathway to automate parameter discovery for nonlinear computational devices.
{"title":"Gradient based optimization of Chaogates","authors":"Anil Radhakrishnan, Sudeshna Sinha, K. Murali, William L. Ditto","doi":"10.1016/j.chaos.2025.116007","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116007","url":null,"abstract":"We present a method for configuring Chaogates to replicate standard Boolean logic gate behavior using gradient-based optimization. By defining a differentiable formulation of the Chaogate encoding, we optimize its tunable parameters to reconfigure the Chaogate for standard logic gate functions. This novel approach allows us to bring the well established tools of machine learning to optimizing Chaogates without the cost of high parameter count neural networks. We further extend this approach to the simultaneous optimization of multiple gates for tuning logic circuits. Experimental results demonstrate the viability of this technique across different nonlinear systems and configurations, offering a pathway to automate parameter discovery for nonlinear computational devices.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"57 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1016/j.chaos.2025.116020
Pradeep G. Siddheshwar, Anoop Suresh, M.S. Jagadeesh Kumar
This paper deals with a weakly nonlinear study of two-dimensional Rayleigh–Bénard magnetoconvection using a simplified five-dimensional Lorenz model. The governing equations of the system are nondimensionalized and formulated in terms of the stream function and the scalar magnetic potential. A five-modal Fourier truncation scheme is employed and the resulting equations are scaled to obtain a five-dimensional autonomous dynamical system. The Hopf-Rayleigh number, signifying Hopf bifurcation, is numerically evaluated from the analysis of weakly nonlinear stability. Chaotic and periodic motions are depicted by plotting bifurcation diagrams, largest Lyapunov exponent (LLE) diagrams and three-dimensional projections of the phase-space. For a fixed set of parameter values, increasing the strength of the applied magnetic field is found to increase the Hopf-Rayleigh number, thereby delaying the destabilization of the system’s equilibrium points. It is shown that while low magnetic field strengths favor the onset of chaotic motion directly from the steady state, stronger magnetic field strengths favor the onset of periodic convection from the steady state prior to the appearance of chaotic motion. We observe here that the applied magnetic field regulates the onset of chaotic and periodic motions in the system and therefore, has a rheostatic control over chaotic and periodic behaviors.
{"title":"Rheostatic effect of a magnetic field on the onset of chaotic and periodic motions in a five-dimensional magnetoconvective Lorenz system","authors":"Pradeep G. Siddheshwar, Anoop Suresh, M.S. Jagadeesh Kumar","doi":"10.1016/j.chaos.2025.116020","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116020","url":null,"abstract":"This paper deals with a weakly nonlinear study of two-dimensional Rayleigh–Bénard magnetoconvection using a simplified five-dimensional Lorenz model. The governing equations of the system are nondimensionalized and formulated in terms of the stream function and the scalar magnetic potential. A five-modal Fourier truncation scheme is employed and the resulting equations are scaled to obtain a five-dimensional autonomous dynamical system. The Hopf-Rayleigh number, signifying Hopf bifurcation, is numerically evaluated from the analysis of weakly nonlinear stability. Chaotic and periodic motions are depicted by plotting bifurcation diagrams, largest Lyapunov exponent (LLE) diagrams and three-dimensional projections of the phase-space. For a fixed set of parameter values, increasing the strength of the applied magnetic field is found to increase the Hopf-Rayleigh number, thereby delaying the destabilization of the system’s equilibrium points. It is shown that while low magnetic field strengths favor the onset of chaotic motion directly from the steady state, stronger magnetic field strengths favor the onset of periodic convection from the steady state prior to the appearance of chaotic motion. We observe here that the applied magnetic field regulates the onset of chaotic and periodic motions in the system and therefore, has a rheostatic control over chaotic and periodic behaviors.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"85 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Corner states are a type of zero-dimensional states formed through symmetry or higher-order topology, typically found in photonic lattices with two or more dimensions. These states are generally protected by the higher-order topology of the lattice and exhibit strong robustness, remaining immune to local defects and perturbations. In this study, we investigate zigzag-zigzag, armchair-armchair, and zigzag-armchair corner states in photonic T-graphene lattices, which are formed by one-dimensional topological phase transitions. Both zigzag and armchair edges are defective, corresponding to the edge states associated with the super-SSH and SSH models, respectively. By altering the coupling coefficients between intracell and intercell waveguides, in-phase and out-of-phase corner modes are formed and generated simultaneously. By calculating the band structures and mode distributions of the lattices and simulating the beam propagation within the T-graphene lattices, we theoretically confirm the existence of these corner states. Additionally, we employ continuous-wave laser writing technology to fabricate the lattices and experimentally verify the presence of these corner states. These corner states can exist at the junctions of defective edges in complex rectangular lattice structures, where they strongly localize light beams and remain resistant to perturbations.
{"title":"Corner states in photonic T-graphene lattices protected by one-dimensional topological phase transition","authors":"Guanhuai Cheng, Chengzhen Lu, Guomei Zhu, Yangjian Cai, Yuanmei Gao, Zengrun Wen","doi":"10.1016/j.chaos.2025.116044","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116044","url":null,"abstract":"Corner states are a type of zero-dimensional states formed through symmetry or higher-order topology, typically found in photonic lattices with two or more dimensions. These states are generally protected by the higher-order topology of the lattice and exhibit strong robustness, remaining immune to local defects and perturbations. In this study, we investigate zigzag-zigzag, armchair-armchair, and zigzag-armchair corner states in photonic T-graphene lattices, which are formed by one-dimensional topological phase transitions. Both zigzag and armchair edges are defective, corresponding to the edge states associated with the super-SSH and SSH models, respectively. By altering the coupling coefficients between intracell and intercell waveguides, in-phase and out-of-phase corner modes are formed and generated simultaneously. By calculating the band structures and mode distributions of the lattices and simulating the beam propagation within the T-graphene lattices, we theoretically confirm the existence of these corner states. Additionally, we employ continuous-wave laser writing technology to fabricate the lattices and experimentally verify the presence of these corner states. These corner states can exist at the junctions of defective edges in complex rectangular lattice structures, where they strongly localize light beams and remain resistant to perturbations.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"9 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-22DOI: 10.1016/j.chaos.2025.116017
Shivam, Teekam Singh, Shivam Rawat, Anupam Singh
The dynamic relationship between predators and prey plays a vital role in upholding equilibrium within the natural environment. Mortality plays a crucial role in maintaining the delicate equilibrium of ecosystems. This paper delves into the consequences of mortality in a predator–prey model that incorporates hydra, the Allee effect, and mutual interference among predators. We first established a crisp predator–prey model and then transformed it into a fuzzy model, representing the control parameters as triangular intuitionistic fuzzy numbers. We transform the fuzzy model into the defuzzified model by applying a graded mean integration technique. This technique allows for efficient solution determination using triangular intuitionistic fuzzy numbers. The theoretical section explores the presence and durability of equilibrium points and Hopf bifurcation on mortality parameters. Living organisms have the ability to move from one place to another, so we created a spatial model based on a crisp model. In order to investigate the impact of random movement of species within a population in an isolated area with different mortality parameters, we employ Turing instability. We confirm the theoretical results using the MATLAB package. The phase trajectories for various initial conditions in both environments are displayed, showcasing the species’ population fluctuations. We use the MATCONT package to illustrate the various scenarios that emerge when we alter the mortality parameters. We calculate the presence of saddle–node (SN), Hopf point (H), and Cusp point (CS) in the model. In addition, our spatial model analysis reveals various spatial structures within the isolated domain, including spots, stripes, and mixed patterns. The results indicate that mortality has a beneficial impact on the prey–predator population, helping to sustain ecological balance.
{"title":"Effects of mortality on a predator–prey model in crisp, fuzzy, and spatial environments: A dynamical approach","authors":"Shivam, Teekam Singh, Shivam Rawat, Anupam Singh","doi":"10.1016/j.chaos.2025.116017","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116017","url":null,"abstract":"The dynamic relationship between predators and prey plays a vital role in upholding equilibrium within the natural environment. Mortality plays a crucial role in maintaining the delicate equilibrium of ecosystems. This paper delves into the consequences of mortality in a predator–prey model that incorporates hydra, the Allee effect, and mutual interference among predators. We first established a crisp predator–prey model and then transformed it into a fuzzy model, representing the control parameters as triangular intuitionistic fuzzy numbers. We transform the fuzzy model into the defuzzified model by applying a graded mean integration technique. This technique allows for efficient solution determination using triangular intuitionistic fuzzy numbers. The theoretical section explores the presence and durability of equilibrium points and Hopf bifurcation on mortality parameters. Living organisms have the ability to move from one place to another, so we created a spatial model based on a crisp model. In order to investigate the impact of random movement of species within a population in an isolated area with different mortality parameters, we employ Turing instability. We confirm the theoretical results using the MATLAB package. The phase trajectories for various initial conditions in both environments are displayed, showcasing the species’ population fluctuations. We use the MATCONT package to illustrate the various scenarios that emerge when we alter the mortality parameters. We calculate the presence of saddle–node (SN), Hopf point (H), and Cusp point (CS) in the model. In addition, our spatial model analysis reveals various spatial structures within the isolated domain, including spots, stripes, and mixed patterns. The results indicate that mortality has a beneficial impact on the prey–predator population, helping to sustain ecological balance.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"74 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-22DOI: 10.1016/j.chaos.2025.116025
P. Rahimkhani, Y. Ordokhani, M. Razzaghi
In this study, we consider a new class of nonlinear integro-differential equations with the Bessel fractional integral-derivative. For solving the considered equations, fractional-order clique functions (FCFs), and some of their properties are introduced. First, we approximate the unknown function and its derivatives/integrals in terms of the FCFs. Then, we substitute these approximations and their derivatives/integrals into the considered equation. The left-sided Bessel fractional derivative/integral (LSBFD/I) of the unknown function is approximated using the properties of the FCFs and LSBFD/I. By collocating the resulting residual function at the well-known shifted Legendre points, we derive a system of nonlinear algebraic equations. In addition, convergence analysis of the proposed approach is discussed. Finally, the presented strategy is applied to some numerical experiments to verify its applicability and accuracy.
{"title":"Fractional-order clique functions to solve left-sided Bessel fractional integro-differential equations","authors":"P. Rahimkhani, Y. Ordokhani, M. Razzaghi","doi":"10.1016/j.chaos.2025.116025","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116025","url":null,"abstract":"In this study, we consider a new class of nonlinear integro-differential equations with the Bessel fractional integral-derivative. For solving the considered equations, fractional-order clique functions (FCFs), and some of their properties are introduced. First, we approximate the unknown function and its derivatives/integrals in terms of the FCFs. Then, we substitute these approximations and their derivatives/integrals into the considered equation. The left-sided Bessel fractional derivative/integral (LSBFD/I) of the unknown function is approximated using the properties of the FCFs and LSBFD/I. By collocating the resulting residual function at the well-known shifted Legendre points, we derive a system of nonlinear algebraic equations. In addition, convergence analysis of the proposed approach is discussed. Finally, the presented strategy is applied to some numerical experiments to verify its applicability and accuracy.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"13 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To address the attitude control problem of biplane tail-sitter unmanned aerial vehicles (BFWTSUAV) during flight mode transitions, which are susceptible to various uncertainties such as unmodeled nonlinear dynamics and external disturbances, this paper proposes an adaptive continuous Quasi-Fixed-Time integral terminal sliding mode controller (ACQFITSMC). The proposed ACQFITSMC combines the advantages of Quasi-Fixed-Time terminal sliding mode, integral sliding mode, and adaptive estimation techniques, ensuring fixed-time convergence of attitude errors, strong robustness, and effective suppression of chattering. Unlike traditional methods, the proposed controller incorporates smooth reference attitude and angular velocity planning, which significantly enhances the system’s dynamic performance, suppressing overshoot and actuator saturation. Theoretical analysis demonstrates that the proposed method guarantees practical stability with fixed-time convergence of the closed-loop system. Comparative simulations with the incremental nonlinear dynamic inversion (INDI) controllers, which are widely used for tail-sitter UAVs and existing fixed-time terminal sliding mode controllers, verify the superior performance of the proposed controller. Finally, outdoor flight experiments validate the practicality and superiority of the proposed controller in real-world applications.11A demo video clips of experiments can be [Online]: https://www.youtube.com/watch?v=39185PB-pfY.
{"title":"Adaptive continuous Quasi-Fixed-Time integral terminal sliding mode attitude control for BiFlying-Wings tail-sitter unmanned aerial vehicles during flight mode transition","authors":"Dong Wang, Zheng Qiao, Guangxin Wu, Jiahui Xu, Xinbiao Pei, Yue Bai","doi":"10.1016/j.chaos.2025.115992","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.115992","url":null,"abstract":"To address the attitude control problem of biplane tail-sitter unmanned aerial vehicles (BFWTSUAV) during flight mode transitions, which are susceptible to various uncertainties such as unmodeled nonlinear dynamics and external disturbances, this paper proposes an adaptive continuous Quasi-Fixed-Time integral terminal sliding mode controller (ACQFITSMC). The proposed ACQFITSMC combines the advantages of Quasi-Fixed-Time terminal sliding mode, integral sliding mode, and adaptive estimation techniques, ensuring fixed-time convergence of attitude errors, strong robustness, and effective suppression of chattering. Unlike traditional methods, the proposed controller incorporates smooth reference attitude and angular velocity planning, which significantly enhances the system’s dynamic performance, suppressing overshoot and actuator saturation. Theoretical analysis demonstrates that the proposed method guarantees practical stability with fixed-time convergence of the closed-loop system. Comparative simulations with the incremental nonlinear dynamic inversion (INDI) controllers, which are widely used for tail-sitter UAVs and existing fixed-time terminal sliding mode controllers, verify the superior performance of the proposed controller. Finally, outdoor flight experiments validate the practicality and superiority of the proposed controller in real-world applications.<ce:cross-ref ref><ce:sup loc=\"post\">1</ce:sup></ce:cross-ref><ce:footnote><ce:label>1</ce:label><ce:note-para view=\"all\">A demo video clips of experiments can be [Online]: <ce:inter-ref xlink:href=\"https://www.youtube.com/watch?v=39185PB-pfY\" xlink:type=\"simple\">https://www.youtube.com/watch?v=39185PB-pfY</ce:inter-ref>.</ce:note-para></ce:footnote>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"20 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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