Pub Date : 2023-05-01DOI: 10.1142/s0218127423500669
António M. Lopes
This paper proposes a technique based on unsupervised machine learning to find phases and phase transitions characterizing the dynamics of global terrorism. A dataset of worldwide terrorist incidents, covering the period from 1970 up to 2019 is analyzed. Multidimensional time-series concerning casualties and events are generated from a public domain database and are interpreted as the state of a complex system. The time-series are sliced, and the segments generated are objects that characterize the dynamical process. The objects are compared with each other by means of several distances and classified by means of the multidimensional scaling (MDS) method. The MDS generates loci of objects, where time is displayed as a parametric variable. The obtained portraits are analyzed in terms of the patterns of objects, characterizing the nature of the system dynamics. Complex dynamics are revealed, with periods resembling chaotic behavior, phases and phase transitions. The results demonstrate that the MDS is an effective tool to analyze global terrorism and can be adopted with other complex systems.
{"title":"Phases and Their Transitions Characterizing the Dynamics of Global Terrorism: A Multidimensional Scaling and Visualization Approach","authors":"António M. Lopes","doi":"10.1142/s0218127423500669","DOIUrl":"https://doi.org/10.1142/s0218127423500669","url":null,"abstract":"This paper proposes a technique based on unsupervised machine learning to find phases and phase transitions characterizing the dynamics of global terrorism. A dataset of worldwide terrorist incidents, covering the period from 1970 up to 2019 is analyzed. Multidimensional time-series concerning casualties and events are generated from a public domain database and are interpreted as the state of a complex system. The time-series are sliced, and the segments generated are objects that characterize the dynamical process. The objects are compared with each other by means of several distances and classified by means of the multidimensional scaling (MDS) method. The MDS generates loci of objects, where time is displayed as a parametric variable. The obtained portraits are analyzed in terms of the patterns of objects, characterizing the nature of the system dynamics. Complex dynamics are revealed, with periods resembling chaotic behavior, phases and phase transitions. The results demonstrate that the MDS is an effective tool to analyze global terrorism and can be adopted with other complex systems.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74634141","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 : 2023-05-01DOI: 10.1142/s0218127423500736
Wang Zhang, Hua Nie, Jianhua Wu
This paper is concerned with a reaction–diffusion–advection chemostat model with two species growing and competing for a single-limited resource. By taking the growth rates of the two species as variable parameters, we study the effect of growth rates on the dynamics of this system. It is found that there exist several critical curves, which may classify the dynamics of this system into three scenarios: (1) extinction of both species; (2) competitive exclusion; (3) coexistence. Moreover, we take numerical approaches to further understand the potential behaviors of the above critical curves and observe that the bistable phenomenon can occur, besides competitive exclusion and coexistence. To further study the effect of advection and diffusion on the dynamics of this system, we present the bifurcation diagrams of positive equilibrium solutions of the single species model and the two-species model with the advection rates and the diffusion rates increasing, respectively. These numerical results indicate that advection and diffusion play a key role in determining the dynamics of two species competing in a flow reactor.
{"title":"A Reaction-Diffusion-Advection Chemostat Model in a Flowing Habitat: Mathematical Analysis and Numerical Simulations","authors":"Wang Zhang, Hua Nie, Jianhua Wu","doi":"10.1142/s0218127423500736","DOIUrl":"https://doi.org/10.1142/s0218127423500736","url":null,"abstract":"This paper is concerned with a reaction–diffusion–advection chemostat model with two species growing and competing for a single-limited resource. By taking the growth rates of the two species as variable parameters, we study the effect of growth rates on the dynamics of this system. It is found that there exist several critical curves, which may classify the dynamics of this system into three scenarios: (1) extinction of both species; (2) competitive exclusion; (3) coexistence. Moreover, we take numerical approaches to further understand the potential behaviors of the above critical curves and observe that the bistable phenomenon can occur, besides competitive exclusion and coexistence. To further study the effect of advection and diffusion on the dynamics of this system, we present the bifurcation diagrams of positive equilibrium solutions of the single species model and the two-species model with the advection rates and the diffusion rates increasing, respectively. These numerical results indicate that advection and diffusion play a key role in determining the dynamics of two species competing in a flow reactor.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90614800","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 : 2023-04-01DOI: 10.1142/s0218127423500591
Jiangbin Chen, Maoan Han
In this paper, we study a class of piecewise smooth near-Hamiltonian systems with piecewise polynomial perturbations. We first give the expression of the first order Melnikov function, and then estimate the number of limit cycles bifurcated from periodic annuluses by Melnikov function method. In addition, we discuss the number of limit cycles that can appear simultaneously near both sides of a generalized homoclinic or generalized double homoclinic loop.
{"title":"Bifurcation of Limit Cycles by Perturbing Piecewise Linear Hamiltonian Systems with Piecewise Polynomials","authors":"Jiangbin Chen, Maoan Han","doi":"10.1142/s0218127423500591","DOIUrl":"https://doi.org/10.1142/s0218127423500591","url":null,"abstract":"In this paper, we study a class of piecewise smooth near-Hamiltonian systems with piecewise polynomial perturbations. We first give the expression of the first order Melnikov function, and then estimate the number of limit cycles bifurcated from periodic annuluses by Melnikov function method. In addition, we discuss the number of limit cycles that can appear simultaneously near both sides of a generalized homoclinic or generalized double homoclinic loop.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89156709","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 : 2023-04-01DOI: 10.1142/s021812742350058x
Ranjan Kumar, R. Mitra
Response, stability, and bifurcation of roll oscillations of a biased ship under regular sea waves are investigated. The primary and subharmonic response branches are traced in the frequency domain employing the Incremental Harmonic Balance (IHB) method with a pseudo-arc-length continuation approach. The stability of periodic responses and bifurcation points are determined by monitoring the eigenvalues of the Floquet transition matrix. The primary and higher-order subharmonic responses experience a cascade of period-doubling bifurcations, eventually culminating in chaotic responses detected by numerical integration (NI) of the equation of motion. Bifurcation diagrams are obtained through the period-doubling route to chaos. Solutions are aided with phase portrait, Poincaré map, time history and Fourier spectrum for better clarity as and when required. Finally, the same ship model is investigated under variable excitation moments that may result from different wave heights in regular seas. The biased ship roll model exhibits primary and subharmonic responses, jump phenomena, coexistence of multiple responses, and chaotically modulated motion. The stable, periodic, and steady-state roll responses obtained by the IHB method are validated by the NI method. Results obtained by both methods are found to agree very well.
{"title":"Stability of Periodic Orbits and Bifurcation Analysis of Ship Roll Oscillations in Regular Sea Waves","authors":"Ranjan Kumar, R. Mitra","doi":"10.1142/s021812742350058x","DOIUrl":"https://doi.org/10.1142/s021812742350058x","url":null,"abstract":"Response, stability, and bifurcation of roll oscillations of a biased ship under regular sea waves are investigated. The primary and subharmonic response branches are traced in the frequency domain employing the Incremental Harmonic Balance (IHB) method with a pseudo-arc-length continuation approach. The stability of periodic responses and bifurcation points are determined by monitoring the eigenvalues of the Floquet transition matrix. The primary and higher-order subharmonic responses experience a cascade of period-doubling bifurcations, eventually culminating in chaotic responses detected by numerical integration (NI) of the equation of motion. Bifurcation diagrams are obtained through the period-doubling route to chaos. Solutions are aided with phase portrait, Poincaré map, time history and Fourier spectrum for better clarity as and when required. Finally, the same ship model is investigated under variable excitation moments that may result from different wave heights in regular seas. The biased ship roll model exhibits primary and subharmonic responses, jump phenomena, coexistence of multiple responses, and chaotically modulated motion. The stable, periodic, and steady-state roll responses obtained by the IHB method are validated by the NI method. Results obtained by both methods are found to agree very well.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78522184","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 : 2023-04-01DOI: 10.1142/s0218127423500542
Yu-Han Tong, Guang Ling, Z. Guan, Qingju Fan, Li Wan
Assessing the complexity of signals or dynamical systems is important in disease diagnosis, mechanical system defect, astronomy analysis, and many other fields. Although entropy measures as complexity estimators have greatly improved, the majority of these measures are quite sensitive to specified parameters and are impacted by short data lengths. This paper proposes a novel entropy algorithm to enhance the existing complexity assessment methods based on classical dispersion entropy (DE) and Rényi entropy (RE) by introducing refined composite multiscale coarse-grained treatment and phase transformation. The proposed refined composite multiscale phase Rényi dispersion entropy (PRRCMDE) addresses the flaws of various existing entropy approaches while still incorporating their merits. Several simulated signals from logistic mapping, AR model, MIX process, and additive WGN periodic signals are adopted to examine the performance of PRRCMDE from multiple perspectives. It demonstrates that the efficacy of the suggested algorithm can be increased by modifying the DE and RE parameters to a reasonable range. As a real-world application, the bearings’ varied fault types and levels can also be recognized clearly.
{"title":"Refined Composite Multiscale Phase Rényi Dispersion Entropy for Complexity Measure","authors":"Yu-Han Tong, Guang Ling, Z. Guan, Qingju Fan, Li Wan","doi":"10.1142/s0218127423500542","DOIUrl":"https://doi.org/10.1142/s0218127423500542","url":null,"abstract":"Assessing the complexity of signals or dynamical systems is important in disease diagnosis, mechanical system defect, astronomy analysis, and many other fields. Although entropy measures as complexity estimators have greatly improved, the majority of these measures are quite sensitive to specified parameters and are impacted by short data lengths. This paper proposes a novel entropy algorithm to enhance the existing complexity assessment methods based on classical dispersion entropy (DE) and Rényi entropy (RE) by introducing refined composite multiscale coarse-grained treatment and phase transformation. The proposed refined composite multiscale phase Rényi dispersion entropy (PRRCMDE) addresses the flaws of various existing entropy approaches while still incorporating their merits. Several simulated signals from logistic mapping, AR model, MIX process, and additive WGN periodic signals are adopted to examine the performance of PRRCMDE from multiple perspectives. It demonstrates that the efficacy of the suggested algorithm can be increased by modifying the DE and RE parameters to a reasonable range. As a real-world application, the bearings’ varied fault types and levels can also be recognized clearly.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85565296","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 : 2023-04-01DOI: 10.1142/s0218127423500621
F. Najm, R. Yafia, M. Aziz-Alaoui
In this paper, we propose a reaction–diffusion mathematical model augmented with self/cross-diffusion in 2D domain which describes the oncolytic virotherapy treatment of a tumor with its growth following the logistic law. The tumor cells are divided into uninfected and infected cells and the virus transmission is supposed to be in a direct mode (from cell to cell). In the absence of cross-diffusion, we establish well posedness of the problem, non-negativity and boundedness of solutions, nonexistence of positive solutions, local and global stability of the nontrivial steady-state and the nonoccurrence of Turing instability. In the presence of cross-diffusion, we prove the occurrence of Turing instability by using the cross-diffusion coefficient of infected cells as a parameter. To have an idea about different patterns, we derive the corresponding amplitude equation by using the nonlinear analysis theory. In the end, we perform some numerical simulations to illustrate the obtained theoretical results.
{"title":"Turing Bifurcation Induced by Cross-Diffusion and Amplitude Equation in Oncolytic Therapeutic Model: Viruses as Anti-Tumor Means","authors":"F. Najm, R. Yafia, M. Aziz-Alaoui","doi":"10.1142/s0218127423500621","DOIUrl":"https://doi.org/10.1142/s0218127423500621","url":null,"abstract":"In this paper, we propose a reaction–diffusion mathematical model augmented with self/cross-diffusion in 2D domain which describes the oncolytic virotherapy treatment of a tumor with its growth following the logistic law. The tumor cells are divided into uninfected and infected cells and the virus transmission is supposed to be in a direct mode (from cell to cell). In the absence of cross-diffusion, we establish well posedness of the problem, non-negativity and boundedness of solutions, nonexistence of positive solutions, local and global stability of the nontrivial steady-state and the nonoccurrence of Turing instability. In the presence of cross-diffusion, we prove the occurrence of Turing instability by using the cross-diffusion coefficient of infected cells as a parameter. To have an idea about different patterns, we derive the corresponding amplitude equation by using the nonlinear analysis theory. In the end, we perform some numerical simulations to illustrate the obtained theoretical results.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86399130","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 : 2023-04-01DOI: 10.1142/S0218127423500633
Xiaoxiong Lu, Eric Yong Xie, Chengqing Li
Periodicity analysis of sequences generated by a deterministic system is a long-standing challenge in both theoretical research and engineering applications. To overcome the inevitable degradation of the logistic map on a finite-precision circuit, its numerical domain is commonly converted from a real number field to a ring or a finite field. This paper studies the period of sequences generated by iterating the logistic map over ring [Formula: see text] from the perspective of its associated functional network, where every number in the ring is considered as a node, and the existing mapping relation between any two nodes is regarded as a directed edge. The complete explicit form of the period of the sequences starting from any initial value is given theoretically and verified experimentally. Moreover, conditions on the control parameter and initial value are derived, ensuring the corresponding sequences to achieve the maximum period over the ring. The results can be used as ground truth for dynamical analysis and cryptographical applications of the logistic map over various domains.
{"title":"Periodicity Analysis of the Logistic Map over Ring ℤ3n","authors":"Xiaoxiong Lu, Eric Yong Xie, Chengqing Li","doi":"10.1142/S0218127423500633","DOIUrl":"https://doi.org/10.1142/S0218127423500633","url":null,"abstract":"Periodicity analysis of sequences generated by a deterministic system is a long-standing challenge in both theoretical research and engineering applications. To overcome the inevitable degradation of the logistic map on a finite-precision circuit, its numerical domain is commonly converted from a real number field to a ring or a finite field. This paper studies the period of sequences generated by iterating the logistic map over ring [Formula: see text] from the perspective of its associated functional network, where every number in the ring is considered as a node, and the existing mapping relation between any two nodes is regarded as a directed edge. The complete explicit form of the period of the sequences starting from any initial value is given theoretically and verified experimentally. Moreover, conditions on the control parameter and initial value are derived, ensuring the corresponding sequences to achieve the maximum period over the ring. The results can be used as ground truth for dynamical analysis and cryptographical applications of the logistic map over various domains.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77222531","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 : 2023-04-01DOI: 10.1142/s0218127423500578
Zi Wang, Jiu Ding, N. Rhee
Let [Formula: see text] be a piecewise increasing mapping satisfying some generalized convexity condition, so that it possesses an invariant density that is a decreasing function. We show that this invariant density can be computed by a family of Markov finite approximations that preserve the monotonicity of integrable functions. We also construct a quadratic spline Markov method and demonstrate its merits numerically.
{"title":"Computing Invariant Densities of a Class of Piecewise Increasing Mappings","authors":"Zi Wang, Jiu Ding, N. Rhee","doi":"10.1142/s0218127423500578","DOIUrl":"https://doi.org/10.1142/s0218127423500578","url":null,"abstract":"Let [Formula: see text] be a piecewise increasing mapping satisfying some generalized convexity condition, so that it possesses an invariant density that is a decreasing function. We show that this invariant density can be computed by a family of Markov finite approximations that preserve the monotonicity of integrable functions. We also construct a quadratic spline Markov method and demonstrate its merits numerically.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88626714","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 : 2023-04-01DOI: 10.1142/s0218127423500645
Mengran Yuan, Na Wang
This work studies a three-dimensional predator–prey model with gestation delay and stage structure between aphidophagous coccinellids and aphid pests, where the interaction between mature coccinellids and aphids is inscribed by Crowley–Martin functional response function, and immature coccinellids and aphids act in the form of Holling-I type. We prove the positivity and boundedness of the solution of the nondelayed system and analyze its equilibrium point, local asymptotic stability, and global stability. In addition to the delays, the critical values of Hopf bifurcation occurring for different parameters are also found from the numerical simulation. The stability of the delayed system and Hopf bifurcation with different delays as parameters are also discussed. Our model analysis shows that the time delay essentially governs the system’s dynamics, and the stability of the system switches as delays increase. We also investigate the direction and stability of the Hopf bifurcation using the normal form theory and center manifold theorem. Finally, we perform computer simulations and depict diagrams to support our theoretical results.
{"title":"Dynamics of a Coccinellids-Aphids Model with Stage Structure in Predator Including Maturation and Gestation Delays","authors":"Mengran Yuan, Na Wang","doi":"10.1142/s0218127423500645","DOIUrl":"https://doi.org/10.1142/s0218127423500645","url":null,"abstract":"This work studies a three-dimensional predator–prey model with gestation delay and stage structure between aphidophagous coccinellids and aphid pests, where the interaction between mature coccinellids and aphids is inscribed by Crowley–Martin functional response function, and immature coccinellids and aphids act in the form of Holling-I type. We prove the positivity and boundedness of the solution of the nondelayed system and analyze its equilibrium point, local asymptotic stability, and global stability. In addition to the delays, the critical values of Hopf bifurcation occurring for different parameters are also found from the numerical simulation. The stability of the delayed system and Hopf bifurcation with different delays as parameters are also discussed. Our model analysis shows that the time delay essentially governs the system’s dynamics, and the stability of the system switches as delays increase. We also investigate the direction and stability of the Hopf bifurcation using the normal form theory and center manifold theorem. Finally, we perform computer simulations and depict diagrams to support our theoretical results.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91055904","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 : 2023-04-01DOI: 10.1142/s0218127423500529
R. K. Tagne, P. Woafo, J. Awrejcewicz
This paper considers the experimental and numerical study of an electromechanical arm powered by a DC motor and subjected to the action of permanent magnets. The magnetic torques arise from permanent magnets mounted at the free end of the arm and along a circle. The electrical subsystem is powered by two forms of input signal (DC and AC voltage sources). For each case, we determine the condition for complete rotation of the mechanical arm versus the parameters of the system such as the arm length, the number of magnets, and the frequency of the external signal. The nonlinear dynamics of the system is examined by means of time-histories, bifurcation diagrams, Lyapunov exponents and phase portraits. Chaotic and periodic dynamics are detected numerically and confirmed experimentally.
{"title":"Dynamics of the Rotating Arm of an Electromechanical System Subjected to the Action of Circularly Placed Magnets: Numerical Study and Experiment","authors":"R. K. Tagne, P. Woafo, J. Awrejcewicz","doi":"10.1142/s0218127423500529","DOIUrl":"https://doi.org/10.1142/s0218127423500529","url":null,"abstract":"This paper considers the experimental and numerical study of an electromechanical arm powered by a DC motor and subjected to the action of permanent magnets. The magnetic torques arise from permanent magnets mounted at the free end of the arm and along a circle. The electrical subsystem is powered by two forms of input signal (DC and AC voltage sources). For each case, we determine the condition for complete rotation of the mechanical arm versus the parameters of the system such as the arm length, the number of magnets, and the frequency of the external signal. The nonlinear dynamics of the system is examined by means of time-histories, bifurcation diagrams, Lyapunov exponents and phase portraits. Chaotic and periodic dynamics are detected numerically and confirmed experimentally.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87707789","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：