Pub Date : 2023-07-01DOI: 10.1142/s0218127423501043
P. Siddheshwar, Ruwaidiah Idris, C. Kanchana, David Laroze
Linear and nonlinear stability analyses of Rayleigh–Bénard convection in water-copper and water-alumina nanofluids are studied in the paper by considering a minimal as well as an extended truncated Fourier representation. These representations respectively result in a third-order classical Lorenz model and a five-dimensional extended Lorenz model. The marginal stability plots reveal that the influence of added dilute concentration of nanoparticles in water is to destabilize the system. The rate of destabilization depends on the nanoparticles’ thermophysical properties and their volume fraction. Influence of adding an additional mode in the horizontal direction is to modify the cell size. This can be observed through the marginal curves as well as the stream line plots. Further, from the Nusselt number plots it is evident that the presence of dilute concentration of nanoparticles in water is to enhance heat transport in the system significantly. The dynamical behavior of the minimal and the extended Lorenz models is investigated using the bifurcation diagram. From the study an important finding that emerges is that the Fourier truncated solution is predicted to have different effects in lower-order and higher-order models. The extended penta-modal Lorenz system predicts advanced onset of chaos compared to that predicted by the classical third-order Lorenz model. The individual influence of both nanoparticles in water is to advance the onset of convection as well as to advance the onset of chaos.
{"title":"Rayleigh-Bénard Convection of Water-Copper and Water-Alumina Nanofluids Based on Minimal- and Higher-Mode Lorenz Models","authors":"P. Siddheshwar, Ruwaidiah Idris, C. Kanchana, David Laroze","doi":"10.1142/s0218127423501043","DOIUrl":"https://doi.org/10.1142/s0218127423501043","url":null,"abstract":"Linear and nonlinear stability analyses of Rayleigh–Bénard convection in water-copper and water-alumina nanofluids are studied in the paper by considering a minimal as well as an extended truncated Fourier representation. These representations respectively result in a third-order classical Lorenz model and a five-dimensional extended Lorenz model. The marginal stability plots reveal that the influence of added dilute concentration of nanoparticles in water is to destabilize the system. The rate of destabilization depends on the nanoparticles’ thermophysical properties and their volume fraction. Influence of adding an additional mode in the horizontal direction is to modify the cell size. This can be observed through the marginal curves as well as the stream line plots. Further, from the Nusselt number plots it is evident that the presence of dilute concentration of nanoparticles in water is to enhance heat transport in the system significantly. The dynamical behavior of the minimal and the extended Lorenz models is investigated using the bifurcation diagram. From the study an important finding that emerges is that the Fourier truncated solution is predicted to have different effects in lower-order and higher-order models. The extended penta-modal Lorenz system predicts advanced onset of chaos compared to that predicted by the classical third-order Lorenz model. The individual influence of both nanoparticles in water is to advance the onset of convection as well as to advance the onset of chaos.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86257266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.1142/s0218127423501031
Changchun Sun
A problem on how to generate chaos from two 3D linear systems via switching control is investigated. Each linear system has the simplest algebraic structure with three parameters. Two basic conditions of all parameters are given. One of two linear systems is stable. The other is unstable. Switching signals of different quadratic surfaces are designed respectively to generate chaotic dynamical behaviors. The constructed quadratic surfaces can be bounded or unbounded. Numerical examples and corresponding simulations verify the feasibility and effectiveness of the designed switching signals of quadratic surfaces for generating chaos.
{"title":"Switching Signals Design for Generating Chaos from Two Linear Systems","authors":"Changchun Sun","doi":"10.1142/s0218127423501031","DOIUrl":"https://doi.org/10.1142/s0218127423501031","url":null,"abstract":"A problem on how to generate chaos from two 3D linear systems via switching control is investigated. Each linear system has the simplest algebraic structure with three parameters. Two basic conditions of all parameters are given. One of two linear systems is stable. The other is unstable. Switching signals of different quadratic surfaces are designed respectively to generate chaotic dynamical behaviors. The constructed quadratic surfaces can be bounded or unbounded. Numerical examples and corresponding simulations verify the feasibility and effectiveness of the designed switching signals of quadratic surfaces for generating chaos.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82656917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.1142/s0218127423501067
Xiaoyuan Chang, Xu Gao, Jimin Zhang
The oscillatory dynamics of a delayed housefly model is analyzed in this paper. The local and global stabilities at the non-negative equilibria are obtained via analyzing the distribution of eigenvalues and Lyapunov–LaSalle invariance principle, and the model undergoes the supercritical Hopf bifurcation and the transient oscillation. Based on Wu’s global Hopf bifurcation theory, the existence of the global bifurcation is established under certain conditions.
{"title":"Hopf Bifurcation Analysis of a Housefly Model with Time Delay","authors":"Xiaoyuan Chang, Xu Gao, Jimin Zhang","doi":"10.1142/s0218127423501067","DOIUrl":"https://doi.org/10.1142/s0218127423501067","url":null,"abstract":"The oscillatory dynamics of a delayed housefly model is analyzed in this paper. The local and global stabilities at the non-negative equilibria are obtained via analyzing the distribution of eigenvalues and Lyapunov–LaSalle invariance principle, and the model undergoes the supercritical Hopf bifurcation and the transient oscillation. Based on Wu’s global Hopf bifurcation theory, the existence of the global bifurcation is established under certain conditions.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83181397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.1142/s0218127423300239
He Xiao, Haohang Sun, Tianhao Zhao, Yue Zhou, Xiaofang Hu
The use of memristive neuromorphic circuit and system is a promising solution for next-generation Artificial Intelligence (AI) computing, as it offers possibilities that go beyond conventional GPU-based artificial neural network computing platforms. However, most of the existing memristive neuromorphic circuits and systems are designed for the specific networks, which is lack of universality and flexibility. Therefore, this paper proposes a universal memristive circuit and system framework for pure-attention-based transformer networks to implement multifunction applications on edge devices. Furthermore, the verification of image recognition and speech recognition was achieved by extending the size of the memristor crossbar array macros and reconfiguring the memristor weights without changing the memristive transformer circuit and framework. This paper not only provides a universal edge implementation framework for multifunction applications of the transformer, but also offers a low-power and promising solution for the application of pure-attention-based transformers on edge devices.
{"title":"Pure-Attention-Based Multifunction Memristive Neuromorphic Circuit and System","authors":"He Xiao, Haohang Sun, Tianhao Zhao, Yue Zhou, Xiaofang Hu","doi":"10.1142/s0218127423300239","DOIUrl":"https://doi.org/10.1142/s0218127423300239","url":null,"abstract":"The use of memristive neuromorphic circuit and system is a promising solution for next-generation Artificial Intelligence (AI) computing, as it offers possibilities that go beyond conventional GPU-based artificial neural network computing platforms. However, most of the existing memristive neuromorphic circuits and systems are designed for the specific networks, which is lack of universality and flexibility. Therefore, this paper proposes a universal memristive circuit and system framework for pure-attention-based transformer networks to implement multifunction applications on edge devices. Furthermore, the verification of image recognition and speech recognition was achieved by extending the size of the memristor crossbar array macros and reconfiguring the memristor weights without changing the memristive transformer circuit and framework. This paper not only provides a universal edge implementation framework for multifunction applications of the transformer, but also offers a low-power and promising solution for the application of pure-attention-based transformers on edge devices.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81722390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.1142/s0218127423501122
L. Ryashko, T. Perevalova, I. Bashkirtseva
A tritrophic “prey-intermediate predator-top predator” population system with disease in the intermediate predator is considered. For this 4D-model, the bifurcation analysis is performed. In this analysis, the rate of the disease transmission is used as a bifurcation parameter. A variety of mono-, bi- and tri-stable behaviors with regular and chaotic attractors are analyzed. It is shown how random disturbances of the bifurcation parameter cause multistage stochastic transformations, noise-induced excitement, and stochastic transitions from order to chaos and reversely. These noise-induced effects are studied in terms of stochastic P- and D-bifurcations.
{"title":"Stochastic Bifurcations and Multistage Order-Chaos Transitions in a 4D Eco-Epidemiological Model","authors":"L. Ryashko, T. Perevalova, I. Bashkirtseva","doi":"10.1142/s0218127423501122","DOIUrl":"https://doi.org/10.1142/s0218127423501122","url":null,"abstract":"A tritrophic “prey-intermediate predator-top predator” population system with disease in the intermediate predator is considered. For this 4D-model, the bifurcation analysis is performed. In this analysis, the rate of the disease transmission is used as a bifurcation parameter. A variety of mono-, bi- and tri-stable behaviors with regular and chaotic attractors are analyzed. It is shown how random disturbances of the bifurcation parameter cause multistage stochastic transformations, noise-induced excitement, and stochastic transitions from order to chaos and reversely. These noise-induced effects are studied in terms of stochastic P- and D-bifurcations.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74299619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.1142/s0218127423501109
Lei Wang, Yu Zhou, Da Xu, Q. Lai
A power system shows chaotic oscillation when it is subjected to periodic load disturbance, which makes it a challenging and interesting problem for stability control of chaotic power system. In this paper, a unified controller is designed to solve the fixed-time and preassigned-time stability problems of fourth-order chaotic power systems. In addition, based on Lyapunov stability theory, sufficient conditions are established for the fixed-time and preassigned-time stability of the underlying chaotic power systems, and a more accurate estimation of the settling time is also derived. Finally, according to numerical simulations, we validate the theoretical results.
{"title":"Fixed-/Preassigned-Time Stability Control of Chaotic Power Systems","authors":"Lei Wang, Yu Zhou, Da Xu, Q. Lai","doi":"10.1142/s0218127423501109","DOIUrl":"https://doi.org/10.1142/s0218127423501109","url":null,"abstract":"A power system shows chaotic oscillation when it is subjected to periodic load disturbance, which makes it a challenging and interesting problem for stability control of chaotic power system. In this paper, a unified controller is designed to solve the fixed-time and preassigned-time stability problems of fourth-order chaotic power systems. In addition, based on Lyapunov stability theory, sufficient conditions are established for the fixed-time and preassigned-time stability of the underlying chaotic power systems, and a more accurate estimation of the settling time is also derived. Finally, according to numerical simulations, we validate the theoretical results.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79655808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.1142/s0218127423501134
J. Andres, Pavel Ludvík
The main purpose of this paper is to investigate a parametric topological entropy for impulsive differential inclusions on tori. In this way, besides other matters, we would like to extend our recent results concerning impulsive differential equations as well as those on “nonparametric” topological entropy to impulsive differential inclusions. Parametric topological entropy, which is usually called a topological entropy for nonautonomous dynamical systems, is considered here via the compositions of associated multivalued Poincaré translation operators with the single-valued time-dependent impulsive maps. On compact polyhedra and, in particular on tori, parametric topological entropy for families of admissible multivalued maps can be estimated from below by means Ivanov-type inequality in terms of the asymptotic Nielsen and Lefschetz numbers which are, unlike the topological entropy, homotopy invariants. In the scalar case, an effective criterion for a positive parametric topological entropy can be given by topological degree arguments for equi-continuous impulsive maps. In a single-valued nonparametric case, a positive topological entropy usually signifies topological chaos. Some simple illustrative examples are provided.
{"title":"Parametric Topological Entropy for Multivalued Maps and Differential Inclusions with Nonautonomous Impulses","authors":"J. Andres, Pavel Ludvík","doi":"10.1142/s0218127423501134","DOIUrl":"https://doi.org/10.1142/s0218127423501134","url":null,"abstract":"The main purpose of this paper is to investigate a parametric topological entropy for impulsive differential inclusions on tori. In this way, besides other matters, we would like to extend our recent results concerning impulsive differential equations as well as those on “nonparametric” topological entropy to impulsive differential inclusions. Parametric topological entropy, which is usually called a topological entropy for nonautonomous dynamical systems, is considered here via the compositions of associated multivalued Poincaré translation operators with the single-valued time-dependent impulsive maps. On compact polyhedra and, in particular on tori, parametric topological entropy for families of admissible multivalued maps can be estimated from below by means Ivanov-type inequality in terms of the asymptotic Nielsen and Lefschetz numbers which are, unlike the topological entropy, homotopy invariants. In the scalar case, an effective criterion for a positive parametric topological entropy can be given by topological degree arguments for equi-continuous impulsive maps. In a single-valued nonparametric case, a positive topological entropy usually signifies topological chaos. Some simple illustrative examples are provided.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84794119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.1142/s0218127423300227
Pedro Haerter, L. Souza, A. C. Mathias, Ricardo L. Viana, I. L. Caldas
The structure of magnetic field lines in toroidal fusion plasmas, as in tokamaks and stellarators, represents the lowest-order description of the plasma particle behavior, up to finite Larmor and drift effects. Tokamaks with reversed magnetic shear typically present internal transport barriers that help to improve confinement through a partial or total reduction of the particle transport across magnetic surfaces. In this work, we investigate numerically particle escape in tokamaks with reversed shear in order to identify fractal structures affecting transport. These structures are quantitatively evaluated using two basic measures: the basin entropy and the Wada property.
{"title":"Basin Entropy and Wada Property of Magnetic Field Line Escape in Toroidal Plasmas with Reversed Shear","authors":"Pedro Haerter, L. Souza, A. C. Mathias, Ricardo L. Viana, I. L. Caldas","doi":"10.1142/s0218127423300227","DOIUrl":"https://doi.org/10.1142/s0218127423300227","url":null,"abstract":"The structure of magnetic field lines in toroidal fusion plasmas, as in tokamaks and stellarators, represents the lowest-order description of the plasma particle behavior, up to finite Larmor and drift effects. Tokamaks with reversed magnetic shear typically present internal transport barriers that help to improve confinement through a partial or total reduction of the particle transport across magnetic surfaces. In this work, we investigate numerically particle escape in tokamaks with reversed shear in order to identify fractal structures affecting transport. These structures are quantitatively evaluated using two basic measures: the basin entropy and the Wada property.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78363245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-30DOI: 10.1142/s0218127423500906
Shaohui Yan, Yu Ren, Binxian Gu, Qiyu Wang, Ertong Wang
In this paper, a four-dimensional chaotic system based on a flux-controlled memristor with cosine function is constructed. It has infinitely many equilibria. By changing the initial values [Formula: see text], [Formula: see text] and [Formula: see text] of the system and keeping the parameters constant, we obtained the distribution of infinitely many single-wing and double-wing attractors along the [Formula: see text]-coordinate, which verifies the initial-offset boosting behavior of the system. Then the complex dynamical behavior of the system is studied in detail through the phase portraits of coexisting attractors, the average value of state variables, Lyapunov exponent spectrum, bifurcation diagram, attraction basin and the complexity of spectral entropy (SE). In addition, the simulation of the Multisim circuit is also carried out, and the results of numerical simulation and analog circuit simulation are consistent. Finally, the chaotic sequence generated by the system is applied to image encryption, and according to the performance analysis, the proposed chaotic system has good security performance.
{"title":"Dynamics and Circuit Implementation of a 4D Memristive Chaotic System with Extreme Multistability","authors":"Shaohui Yan, Yu Ren, Binxian Gu, Qiyu Wang, Ertong Wang","doi":"10.1142/s0218127423500906","DOIUrl":"https://doi.org/10.1142/s0218127423500906","url":null,"abstract":"In this paper, a four-dimensional chaotic system based on a flux-controlled memristor with cosine function is constructed. It has infinitely many equilibria. By changing the initial values [Formula: see text], [Formula: see text] and [Formula: see text] of the system and keeping the parameters constant, we obtained the distribution of infinitely many single-wing and double-wing attractors along the [Formula: see text]-coordinate, which verifies the initial-offset boosting behavior of the system. Then the complex dynamical behavior of the system is studied in detail through the phase portraits of coexisting attractors, the average value of state variables, Lyapunov exponent spectrum, bifurcation diagram, attraction basin and the complexity of spectral entropy (SE). In addition, the simulation of the Multisim circuit is also carried out, and the results of numerical simulation and analog circuit simulation are consistent. Finally, the chaotic sequence generated by the system is applied to image encryption, and according to the performance analysis, the proposed chaotic system has good security performance.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84173561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-30DOI: 10.1142/s0218127423500980
Jianglong Xiao, Yonghui Xia
In this paper, we study one type of predator–prey model with simplified Holling type IV functional response by incorporating the fear effect into prey species. The existence and stability of all equilibria of the system are studied. And bifurcation behaviors including saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation of the system are completely explored. Numerical simulation is carried out to illustrate the theoretical analysis. It is shown that the fear effect does affect some dynamic behaviors of the system. Finally, we summarize the findings in a conclusion.
{"title":"Global Dynamics of a Predator-Prey Model with Simplified Holling Type IV Functional Response and Fear Effect","authors":"Jianglong Xiao, Yonghui Xia","doi":"10.1142/s0218127423500980","DOIUrl":"https://doi.org/10.1142/s0218127423500980","url":null,"abstract":"In this paper, we study one type of predator–prey model with simplified Holling type IV functional response by incorporating the fear effect into prey species. The existence and stability of all equilibria of the system are studied. And bifurcation behaviors including saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation of the system are completely explored. Numerical simulation is carried out to illustrate the theoretical analysis. It is shown that the fear effect does affect some dynamic behaviors of the system. Finally, we summarize the findings in a conclusion.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86919101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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