Pub Date : 2023-06-15DOI: 10.1142/S0218127423500797
J. Zhang, Mengran Nan, Lixiang Wei, Xinlei An, Meijuan He
In this paper, a wind turbine generator drive system with stochastic excitation under both displacement and velocity delayed feedback is considered. Firstly, the center manifold method is used to approximate the delay term of the system, so that the Itô-stochastic differential equation can be obtained by random average method. Through the maximal Lyapunov exponential method, the local stochastic stability and random D-bifurcation conditions of the system are obtained. Secondly, it is verified that the increase of noise intensity and delay value induces the occurrence of random P-bifurcation of the system through Monte Carlo numerical simulations. In addition, the theoretical chaos threshold of the system is derived by the random Melnikov method. The results show that the chaos threshold decreases as the noise intensity increases, and the increase in time delay leads to a delay in the chaotic behavior of the system. Finally, the correctness and effectiveness of the chaos-theoretic analysis are verified based on the one-parameter bifurcation diagrams and the two-parameter bifurcation diagrams.
{"title":"Bifurcation Analysis of a Wind Turbine Generator Drive System with Stochastic Excitation Under Both Displacement and Velocity Delayed Feedback","authors":"J. Zhang, Mengran Nan, Lixiang Wei, Xinlei An, Meijuan He","doi":"10.1142/S0218127423500797","DOIUrl":"https://doi.org/10.1142/S0218127423500797","url":null,"abstract":"In this paper, a wind turbine generator drive system with stochastic excitation under both displacement and velocity delayed feedback is considered. Firstly, the center manifold method is used to approximate the delay term of the system, so that the Itô-stochastic differential equation can be obtained by random average method. Through the maximal Lyapunov exponential method, the local stochastic stability and random D-bifurcation conditions of the system are obtained. Secondly, it is verified that the increase of noise intensity and delay value induces the occurrence of random P-bifurcation of the system through Monte Carlo numerical simulations. In addition, the theoretical chaos threshold of the system is derived by the random Melnikov method. The results show that the chaos threshold decreases as the noise intensity increases, and the increase in time delay leads to a delay in the chaotic behavior of the system. Finally, the correctness and effectiveness of the chaos-theoretic analysis are verified based on the one-parameter bifurcation diagrams and the two-parameter bifurcation diagrams.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91467179","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 : 2023-06-15DOI: 10.1142/S0218127423300173
Y. Horikawa
Chaotic oscillations induced by single rectification in networks of linear neuron-like elements are examined on three prototype models: one nonautonomous system and two autonomous systems. The first is a system of coupled neurons with periodic input; the second is a system of three coupled neurons with six couplings; the third is a ring of four unidirectionally coupled neurons with one reverse coupling. In each system, the output function of one neuron is ramp and that of the others is linear. Each system is piecewise linear and the phase space is separated into two domains by a single border. Steady states, periodic solutions and homoclinic orbits are derived rigorously and their stability is evaluated with the eigenvalues of the Jacobian matrices. The bifurcation analysis of the three systems shows that chaotic attractors could be generated through cascades of period-doubling bifurcations of periodic solutions.
{"title":"Minimal Chaotic Networks of Linear Neuron-Like Elements with Single Rectification: Three Prototypes","authors":"Y. Horikawa","doi":"10.1142/S0218127423300173","DOIUrl":"https://doi.org/10.1142/S0218127423300173","url":null,"abstract":"Chaotic oscillations induced by single rectification in networks of linear neuron-like elements are examined on three prototype models: one nonautonomous system and two autonomous systems. The first is a system of coupled neurons with periodic input; the second is a system of three coupled neurons with six couplings; the third is a ring of four unidirectionally coupled neurons with one reverse coupling. In each system, the output function of one neuron is ramp and that of the others is linear. Each system is piecewise linear and the phase space is separated into two domains by a single border. Steady states, periodic solutions and homoclinic orbits are derived rigorously and their stability is evaluated with the eigenvalues of the Jacobian matrices. The bifurcation analysis of the three systems shows that chaotic attractors could be generated through cascades of period-doubling bifurcations of periodic solutions.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89081720","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}
We analyze the dynamics of a class of [Formula: see text]-equivariant Hamiltonian systems of the form [Formula: see text], where [Formula: see text] is complex, the time [Formula: see text] is real, while [Formula: see text] and [Formula: see text] are real parameters. The topological phase portraits with at least one center are given. The finite generators of Abelian integral [Formula: see text] are obtained, where [Formula: see text] is a family of closed ovals defined by [Formula: see text] [Formula: see text], [Formula: see text] is the open interval on which [Formula: see text] is defined, [Formula: see text], [Formula: see text] are real polynomials in [Formula: see text] and [Formula: see text] with degree [Formula: see text]. We give an estimation of the number of isolated zeros of the corresponding Abelian integral by using its algebraic structure. We show that for the given polynomials [Formula: see text] and [Formula: see text] in [Formula: see text] and [Formula: see text] with degree [Formula: see text], the number of the limit cycles of the perturbed [Formula: see text]-equivariant Hamiltonian system does not exceed [Formula: see text] (taking into account the multiplicity).
{"title":"Estimating the Number of Zeros of Abelian Integrals for the Perturbed Cubic Z4-Equivariant Planar Hamiltonian System","authors":"Aiyong Chen, Wentao Huang, Yonghui Xia, Huiyang Zhang","doi":"10.1142/S0218127423500852","DOIUrl":"https://doi.org/10.1142/S0218127423500852","url":null,"abstract":"We analyze the dynamics of a class of [Formula: see text]-equivariant Hamiltonian systems of the form [Formula: see text], where [Formula: see text] is complex, the time [Formula: see text] is real, while [Formula: see text] and [Formula: see text] are real parameters. The topological phase portraits with at least one center are given. The finite generators of Abelian integral [Formula: see text] are obtained, where [Formula: see text] is a family of closed ovals defined by [Formula: see text] [Formula: see text], [Formula: see text] is the open interval on which [Formula: see text] is defined, [Formula: see text], [Formula: see text] are real polynomials in [Formula: see text] and [Formula: see text] with degree [Formula: see text]. We give an estimation of the number of isolated zeros of the corresponding Abelian integral by using its algebraic structure. We show that for the given polynomials [Formula: see text] and [Formula: see text] in [Formula: see text] and [Formula: see text] with degree [Formula: see text], the number of the limit cycles of the perturbed [Formula: see text]-equivariant Hamiltonian system does not exceed [Formula: see text] (taking into account the multiplicity).","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90072136","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 : 2023-06-15DOI: 10.1142/S0218127423500840
Cong Ding, Ru Xue, Shi-Jin Niu
Biometric images are an important means of personal identity verification and identification and are related to personal privacy and property security. To address the problems of poor security and low image reconstruction quality in the encryption and transmission of multibiometric images, a multibiometric images encryption method based on Fast Fourier Transform (FFT) and hyperchaotic system is proposed. First, the FFT is used to transform the multibiometric images from spatial to frequency domain. Then, the initial values of the hyperchaotic Lorenz system are generated using a one-dimensional chaotic logistic system to generate the key stream. Combined with the recoding rules of matrix reconstruction and scrambling without repetition of using multimatrix, the multiple matrices of amplitude and phase in the transform domain are reconstructed to be multiple RGB three-channel color images by using the inverse fast Fourier transform. Then, we combine the two diffusion methods of additive mode and Galois domain diffusion on each color channel to perform confusion and diffusion. Finally, the multiple grayscale images are encrypted to become multiple color images. The experimental results demonstrate that the method can effectively defend against various attacks. In addition, it solves the problem of low reconstruction accuracy that exists in the field of multiple images security.
{"title":"Multibiometric Images Encryption Method Based on Fast Fourier Transform and Hyperchaos","authors":"Cong Ding, Ru Xue, Shi-Jin Niu","doi":"10.1142/S0218127423500840","DOIUrl":"https://doi.org/10.1142/S0218127423500840","url":null,"abstract":"Biometric images are an important means of personal identity verification and identification and are related to personal privacy and property security. To address the problems of poor security and low image reconstruction quality in the encryption and transmission of multibiometric images, a multibiometric images encryption method based on Fast Fourier Transform (FFT) and hyperchaotic system is proposed. First, the FFT is used to transform the multibiometric images from spatial to frequency domain. Then, the initial values of the hyperchaotic Lorenz system are generated using a one-dimensional chaotic logistic system to generate the key stream. Combined with the recoding rules of matrix reconstruction and scrambling without repetition of using multimatrix, the multiple matrices of amplitude and phase in the transform domain are reconstructed to be multiple RGB three-channel color images by using the inverse fast Fourier transform. Then, we combine the two diffusion methods of additive mode and Galois domain diffusion on each color channel to perform confusion and diffusion. Finally, the multiple grayscale images are encrypted to become multiple color images. The experimental results demonstrate that the method can effectively defend against various attacks. In addition, it solves the problem of low reconstruction accuracy that exists in the field of multiple images security.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90761983","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}
Recently, spatial memory and Allee effect have been widely investigated in population models, independently. This paper introduces these two aspects to a predator–prey system, and studies the interaction of two species. Allee effect causes bistability, and the predator-free steady-state is always locally stable. Prey-taxis can play a stable role in positive constant steady-state, and spatial memory delay generates the inhomogeneous Hopf bifurcation and even stability switching. In the absence of spatial memory delay, the stronger the predator is subject to the Allee effect, the larger the prey-taxis coefficient is required to keep two species coexist in a stable spatially homogenous form. With the same prey-taxis coefficient, the critical threshold of spatial memory delay corresponding to large predator diffusion coefficient is distinctly bigger than the one corresponding to small predator diffusion coefficient. Moreover, the amplitudes of spatial patterns, which reflect the degree of inhomogeneity, oscillate as spatial memory delay varies.
{"title":"Impact of Spatial Memory on a Predator-Prey System with Allee Effect","authors":"Daiyong Wu, Fengping Lu, Chuansheng Shen, Jian Gao","doi":"10.1142/s0218127423500864","DOIUrl":"https://doi.org/10.1142/s0218127423500864","url":null,"abstract":"Recently, spatial memory and Allee effect have been widely investigated in population models, independently. This paper introduces these two aspects to a predator–prey system, and studies the interaction of two species. Allee effect causes bistability, and the predator-free steady-state is always locally stable. Prey-taxis can play a stable role in positive constant steady-state, and spatial memory delay generates the inhomogeneous Hopf bifurcation and even stability switching. In the absence of spatial memory delay, the stronger the predator is subject to the Allee effect, the larger the prey-taxis coefficient is required to keep two species coexist in a stable spatially homogenous form. With the same prey-taxis coefficient, the critical threshold of spatial memory delay corresponding to large predator diffusion coefficient is distinctly bigger than the one corresponding to small predator diffusion coefficient. Moreover, the amplitudes of spatial patterns, which reflect the degree of inhomogeneity, oscillate as spatial memory delay varies.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86140201","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 : 2023-06-15DOI: 10.1142/S0218127423500785
Luyao Yan, Honghui Zhang, Zhongkui Sun, Zilu Cao, Zhuan Shen, Lin Du
Epileptic seizures have spatial features related to the propagation of seizure waves. As the main characteristic of absence seizures, 2–4[Formula: see text]Hz spike-wave discharges (SWDs) originate from the cortices and are maintained by the thalamus. In this study, we explore the onset and propagation effect of absence seizures based on a thalamocortical model. First, we develop a two-compartment model and consider the autapse of the thalamic reticular nucleus as a crucial parameter to investigate transition behaviors. Moreover, we present dynamical mechanisms through bifurcation analysis. Simulation results show that the absence seizures can be induced and advanced as the coupling strength increases. Second, we investigate excitatory and inhibitory coupling functions in a three-compartment model. Our research indicates that the excitatory coupling function can lead to SWDs when all the compartments are initially saturated. In the process of propagation, excitatory coupling also gives rise to SWDs in normal compartments, whereas inhibitory coupling plays a limited role. Finally, we reproduce the above results in a 10-compartment model and verify the robustness against the variation of the number of modules. This work may shed new light on the field of seizure propagation and provide potential dynamical mechanisms.
{"title":"Propagation Effect of Epileptic Seizures in a Coupled Thalamocortical Network","authors":"Luyao Yan, Honghui Zhang, Zhongkui Sun, Zilu Cao, Zhuan Shen, Lin Du","doi":"10.1142/S0218127423500785","DOIUrl":"https://doi.org/10.1142/S0218127423500785","url":null,"abstract":"Epileptic seizures have spatial features related to the propagation of seizure waves. As the main characteristic of absence seizures, 2–4[Formula: see text]Hz spike-wave discharges (SWDs) originate from the cortices and are maintained by the thalamus. In this study, we explore the onset and propagation effect of absence seizures based on a thalamocortical model. First, we develop a two-compartment model and consider the autapse of the thalamic reticular nucleus as a crucial parameter to investigate transition behaviors. Moreover, we present dynamical mechanisms through bifurcation analysis. Simulation results show that the absence seizures can be induced and advanced as the coupling strength increases. Second, we investigate excitatory and inhibitory coupling functions in a three-compartment model. Our research indicates that the excitatory coupling function can lead to SWDs when all the compartments are initially saturated. In the process of propagation, excitatory coupling also gives rise to SWDs in normal compartments, whereas inhibitory coupling plays a limited role. Finally, we reproduce the above results in a 10-compartment model and verify the robustness against the variation of the number of modules. This work may shed new light on the field of seizure propagation and provide potential dynamical mechanisms.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91102788","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 : 2023-06-15DOI: 10.1142/s0218127423500839
Lei Wang, Xiao-Song Yang
For a class of three-dimensional piecewise linear systems with an admissible saddle-focus, the existence of three kinds of homoclinic loops is shown. Moreover, the birth and number of the periodic orbits induced by homoclinic bifurcation are investigated, and various sufficient conditions are obtained to guarantee the appearance of only one periodic orbit, finitely many periodic orbits or countably infinitely many periodic orbits. Furthermore, the stability of these newborn periodic orbits is analyzed in detail and some conclusions are made about them to be periodic saddle orbits or periodic sinks. Finally, some examples are given.
{"title":"Existence, Number and Stability of Periodic Orbits Induced by Homoclinic Loops in Three-Dimensional Piecewise Linear Systems with an Admissible Saddle-Focus","authors":"Lei Wang, Xiao-Song Yang","doi":"10.1142/s0218127423500839","DOIUrl":"https://doi.org/10.1142/s0218127423500839","url":null,"abstract":"For a class of three-dimensional piecewise linear systems with an admissible saddle-focus, the existence of three kinds of homoclinic loops is shown. Moreover, the birth and number of the periodic orbits induced by homoclinic bifurcation are investigated, and various sufficient conditions are obtained to guarantee the appearance of only one periodic orbit, finitely many periodic orbits or countably infinitely many periodic orbits. Furthermore, the stability of these newborn periodic orbits is analyzed in detail and some conclusions are made about them to be periodic saddle orbits or periodic sinks. Finally, some examples are given.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86277664","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/s021812742350075x
Ting Chen, Lihong Huang, J. Llibre
During the last twenty years there has been increasing interest in studying the piecewise differential systems, mainly due to their many applications in natural science and technology. Up to now the most studied differential systems are in dimension two, here we study them in dimension three. One of the main difficulties for studying these differential systems consists in controlling the existence and nonexistence of limit cycles, and the numbers when they exist. In this paper, we study the nonsymmetric limit cycles for a family of three-dimensional piecewise linear differential systems with three zones separated by two parallel planes. For this class of differential systems we study the nonexistence, existence and uniqueness of their limit cycles.
{"title":"Nonexistence and Uniqueness of Limit Cycles in a Class of Three-Dimensional Piecewise Linear Differential Systems","authors":"Ting Chen, Lihong Huang, J. Llibre","doi":"10.1142/s021812742350075x","DOIUrl":"https://doi.org/10.1142/s021812742350075x","url":null,"abstract":"During the last twenty years there has been increasing interest in studying the piecewise differential systems, mainly due to their many applications in natural science and technology. Up to now the most studied differential systems are in dimension two, here we study them in dimension three. One of the main difficulties for studying these differential systems consists in controlling the existence and nonexistence of limit cycles, and the numbers when they exist. In this paper, we study the nonsymmetric limit cycles for a family of three-dimensional piecewise linear differential systems with three zones separated by two parallel planes. For this class of differential systems we study the nonexistence, existence and uniqueness of their limit cycles.","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":"74098147","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/s0218127423500670
K. Koubaâ, N. Derbel
Deoxyribonucleic Acid (DNA) coding technology is a new research field developed by the combination of computer science and molecular biology, that has been gradually applied in the field of image encryption in recent years. Furthermore, sensitivity to initial conditions, pseudo-random properties, and state ergodicity of coupled chaotic maps can help produce good pseudo-random number generators and meet the requirements of an image encryption system well. In this paper, an image encryption algorithm based on high-dimensional coupled chaotic maps and DNA coding is proposed. A pseudo-random sequence is generated by a long short-term memory (LSTM) architecture using the proposed maps and evaluated through a set of statistical tests to show the high performance of the proposed generator. All intensity values of an input image are converted to a binary sequence, which is scrambled globally by the high-dimensional coupled chaotic maps. The DNA operations are performed on the scrambled binary sequences instead of binary operations to increase the algorithm efficiency. Simulation results and performance analyses demonstrate that the proposed encryption scheme is extremely sensitive to small changes in secret keys, provides high security and can resist differential attack.
{"title":"DNA Image Encryption Scheme Based on a Chaotic LSTM Pseudo-Random Number Generator","authors":"K. Koubaâ, N. Derbel","doi":"10.1142/s0218127423500670","DOIUrl":"https://doi.org/10.1142/s0218127423500670","url":null,"abstract":"Deoxyribonucleic Acid (DNA) coding technology is a new research field developed by the combination of computer science and molecular biology, that has been gradually applied in the field of image encryption in recent years. Furthermore, sensitivity to initial conditions, pseudo-random properties, and state ergodicity of coupled chaotic maps can help produce good pseudo-random number generators and meet the requirements of an image encryption system well. In this paper, an image encryption algorithm based on high-dimensional coupled chaotic maps and DNA coding is proposed. A pseudo-random sequence is generated by a long short-term memory (LSTM) architecture using the proposed maps and evaluated through a set of statistical tests to show the high performance of the proposed generator. All intensity values of an input image are converted to a binary sequence, which is scrambled globally by the high-dimensional coupled chaotic maps. The DNA operations are performed on the scrambled binary sequences instead of binary operations to increase the algorithm efficiency. Simulation results and performance analyses demonstrate that the proposed encryption scheme is extremely sensitive to small changes in secret keys, provides high security and can resist differential attack.","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":"90600318","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/s0218127423500724
M. Momeni
The stochastic nature of magnetization dynamics of dipole–dipole interactions described by the Landau–Lifshitz–Gilbert equation without considering the Gilbert damping parameter is investigated. It is shown that the occurrence of the complex dynamic states depends on the spatial anisotropy of interactions on one hand and the lattice geometry on the other. It is observed from the higher-order moments of the magnetization fluctuations that two significant dynamical regimes, regular and chaos, may be obtained depending on the perturbation strength. Relying on the Hurst exponent obtained by the standard deviation principle, the correlation and persistence of the magnetization fluctuations are analyzed. The results also exhibit a transition from an anti-correlated to a positively correlated system as the relevant parameters of the system vary.
{"title":"Spin Chaos Dynamics in Classical Random Dipolar Interactions","authors":"M. Momeni","doi":"10.1142/s0218127423500724","DOIUrl":"https://doi.org/10.1142/s0218127423500724","url":null,"abstract":"The stochastic nature of magnetization dynamics of dipole–dipole interactions described by the Landau–Lifshitz–Gilbert equation without considering the Gilbert damping parameter is investigated. It is shown that the occurrence of the complex dynamic states depends on the spatial anisotropy of interactions on one hand and the lattice geometry on the other. It is observed from the higher-order moments of the magnetization fluctuations that two significant dynamical regimes, regular and chaos, may be obtained depending on the perturbation strength. Relying on the Hurst exponent obtained by the standard deviation principle, the correlation and persistence of the magnetization fluctuations are analyzed. The results also exhibit a transition from an anti-correlated to a positively correlated system as the relevant parameters of the system vary.","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":"86757353","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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