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Durairaj P, Kanagaraj S, Duraisamy P, Karthikeyan A, Rajagopal K. Impact of external excitations on blinking enhanced synchronization in bistable vibrational energy harvesters. CHAOS (WOODBURY, N.Y.) 2023; 33:2894475. [PMID: 37276559 DOI: 10.1063/5.0137668] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2022] [Accepted: 05/08/2023] [Indexed: 06/07/2023]
Abstract
Vibrational energy harvesters are capable of converting low-frequency broad-band mechanical energy into electrical power and can be used in implantable medical devices and wireless sensors. With the use of such energy harvesters, it is feasible to generate continuous power that is more reliable and cost-effective. According to previous findings, the energy harvester can offer rich complex dynamics, one of which is obtaining the synchronization behavior, which is intriguing to achieve desirable power from energy harvesters. Therefore, we consider bistable energy harvesters with periodic and quasiperiodic excitations to investigate synchronization. Specifically, we introduce blinking into the coupling function to check whether it improves the synchronization. Interestingly, we discover that raising the normalized proportion of blinking can initiate synchronization behaviors even with lower optimal coupling strength than the absence of blinking in the coupling (i.e., continuous coupling). The existence of synchronization behaviors is confirmed by finding the largest Lyapunov exponents. In addition, the results show that the optimal coupling strength needed to achieve synchronization for quasiperiodic excitations is smaller than that for periodic excitations.
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Affiliation(s)
- Premraj Durairaj
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, Tamilnadu, India
| | - Sathiyadevi Kanagaraj
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, Tamilnadu, India
| | - Prakash Duraisamy
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, Tamilnadu, India
| | - Anitha Karthikeyan
- Department of Electronics and Communication Engineering, University Centre for Research and Development, Chandigarh University, Mohali 140 413, Punjab, India
- Department of Electronics and Communication Engineering, Vemu Institute of Technology, Chittoor, Andhra Pradesh 517112, India
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, Tamilnadu, India
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Parastesh F, Rajagopal K, Jafari S, Perc M, Schöll E. Blinking coupling enhances network synchronization. Phys Rev E 2022; 105:054304. [PMID: 35706266 DOI: 10.1103/physreve.105.054304] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Accepted: 04/13/2022] [Indexed: 06/15/2023]
Abstract
This paper studies the synchronization of a network with linear diffusive coupling, which blinks between the variables periodically. The synchronization of the blinking network in the case of sufficiently fast blinking is analyzed by showing that the stability of the synchronous solution depends only on the averaged coupling and not on the instantaneous coupling. To illustrate the effect of the blinking period on the network synchronization, the Hindmarsh-Rose model is used as the dynamics of nodes. The synchronization is investigated by considering constant single-variable coupling, averaged coupling, and blinking coupling through a linear stability analysis. It is observed that by decreasing the blinking period, the required coupling strength for synchrony is reduced. It equals that of the averaged coupling model times the number of variables. However, in the averaged coupling, all variables participate in the coupling, while in the blinking model only one variable is coupled at any time. Therefore, the blinking coupling leads to an enhanced synchronization in comparison with the single-variable coupling. Numerical simulations of the average synchronization error of the network confirm the results obtained from the linear stability analysis.
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Affiliation(s)
- Fatemeh Parastesh
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Iran
| | | | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Iran
- Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Iran
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, 2000 Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, D-10115 Berlin, Germany
- Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, D-14473 Potsdam, Germany
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Adelakun AO, Ogunjo ST, Fuwape IA. Chaos suppression in fractional order systems using state-dependent noise. SN APPLIED SCIENCES 2019. [DOI: 10.1007/s42452-019-1599-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
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Zhou S, Guo Y, Liu M, Lai YC, Lin W. Random temporal connections promote network synchronization. Phys Rev E 2019; 100:032302. [PMID: 31639942 DOI: 10.1103/physreve.100.032302] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2018] [Indexed: 06/10/2023]
Abstract
We report a phenomenon of collective dynamics on discrete-time complex networks: a random temporal interaction matrix even of zero or/and small average is able to significantly enhance synchronization with probability one. According to current knowledge, there is no verifiably sufficient criterion for the phenomenon. We use the standard method of synchronization analytics and the theory of stochastic processes to establish a criterion, by which we rigorously and accurately depict how synchronization occurring with probability one is affected by the statistical characteristics of the random temporal connections such as the strength and topology of the connections as well as their probability distributions. We also illustrate the enhancement phenomenon using physical and biological complex dynamical networks.
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Affiliation(s)
- Shijie Zhou
- Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China
- School of Mathematical Science, Fudan University, Shanghai 200433, China
- Shanghai Center of Mathematical Sciences, Shanghai 200433, China
| | - Yao Guo
- Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai 200433, China
| | - Maoxing Liu
- Department of Mathematics, North University of China, Taiyuan 030051, China
| | - Ying-Cheng Lai
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287-5706, USA
| | - Wei Lin
- Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China
- School of Mathematical Science, Fudan University, Shanghai 200433, China
- Shanghai Center of Mathematical Sciences, Shanghai 200433, China
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai 200433, China
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5
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Pillai N, Craig M, Dokoumetzidis A, Schwartz SL, Bies R, Freedman I. Chaos synchronization and Nelder-Mead search for parameter estimation in nonlinear pharmacological systems: Estimating tumor antigenicity in a model of immunotherapy. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2018; 139:23-30. [PMID: 29928905 DOI: 10.1016/j.pbiomolbio.2018.06.006] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2018] [Revised: 06/11/2018] [Accepted: 06/13/2018] [Indexed: 11/29/2022]
Abstract
In mathematical pharmacology, models are constructed to confer a robust method for optimizing treatment. The predictive capability of pharmacological models depends heavily on the ability to track the system and to accurately determine parameters with reference to the sensitivity in projected outcomes. To closely track chaotic systems, one may choose to apply chaos synchronization. An advantageous byproduct of this methodology is the ability to quantify model parameters. In this paper, we illustrate the use of chaos synchronization combined with Nelder-Mead search to estimate parameters of the well-known Kirschner-Panetta model of IL-2 immunotherapy from noisy data. Chaos synchronization with Nelder-Mead search is shown to provide more accurate and reliable estimates than Nelder-Mead search based on an extended least squares (ELS) objective function. Our results underline the strength of this approach to parameter estimation and provide a broader framework of parameter identification for nonlinear models in pharmacology.
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Affiliation(s)
- Nikhil Pillai
- University at Buffalo, State University of New York, USA.
| | | | | | | | - Robert Bies
- University at Buffalo, State University of New York, USA.
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Guo Q, Wan F. Complete synchronization of the global coupled dynamical network induced by Poisson noises. PLoS One 2017; 12:e0188632. [PMID: 29216214 PMCID: PMC5720815 DOI: 10.1371/journal.pone.0188632] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2017] [Accepted: 11/11/2017] [Indexed: 11/18/2022] Open
Abstract
The different Poisson noise-induced complete synchronization of the global coupled dynamical network is investigated. Based on the stability theory of stochastic differential equations driven by Poisson process, we can prove that Poisson noises can induce synchronization and sufficient conditions are established to achieve complete synchronization with probability 1. Furthermore, numerical examples are provided to show the agreement between theoretical and numerical analysis.
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Affiliation(s)
- Qing Guo
- School of Aeronautics, Northwestern Polytechnical University, Xi’an, Shaanxi, China
| | - Fangyi Wan
- School of Aeronautics, Northwestern Polytechnical University, Xi’an, Shaanxi, China
- * E-mail:
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Lin W, Chen X, Zhou S. Achieving control and synchronization merely through a stochastically adaptive feedback coupling. CHAOS (WOODBURY, N.Y.) 2017; 27:073110. [PMID: 28764397 DOI: 10.1063/1.4994178] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Techniques of deterministically adaptive feedback couplings have been successfully and extensively applied to realize control or/and synchronization in chaotic dynamical systems and even in complex dynamical networks. In this article, a technique of stochastically adaptive feedback coupling is novelly proposed to not only realize control in chaotic dynamical systems but also achieve synchronization in unidirectionally coupled systems. Compared with those deterministically adaptive couplings, the proposed stochastic technique interestingly shows some advantages from a physical viewpoint of time and energy consumptions. More significantly, the usefulness of the proposed stochastic technique is analytically validated by the theory of stochastic processes. It is anticipated that the proposed stochastic technique will be widely used in achieving system control and network synchronization.
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Affiliation(s)
- Wei Lin
- School of Mathematical Sciences and Centre for Computational Systems Biology of ISTBI, Fudan University, Shanghai 200433, China
| | - Xin Chen
- School of Mathematical Sciences and Centre for Computational Systems Biology of ISTBI, Fudan University, Shanghai 200433, China
| | - Shijie Zhou
- School of Mathematical Sciences and Centre for Computational Systems Biology of ISTBI, Fudan University, Shanghai 200433, China
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Guo Y, Lin W, Ho DWC. Discrete-time systems with random switches: From systems stability to networks synchronization. CHAOS (WOODBURY, N.Y.) 2016; 26:033113. [PMID: 27036191 DOI: 10.1063/1.4944618] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In this article, we develop some approaches, which enable us to more accurately and analytically identify the essential patterns that guarantee the almost sure stability of discrete-time systems with random switches. We allow for the case that the elements in the switching connection matrix even obey some unbounded and continuous-valued distributions. In addition to the almost sure stability, we further investigate the almost sure synchronization in complex dynamical networks consisting of randomly connected nodes. Numerical examples illustrate that a chaotic dynamics in the synchronization manifold is preserved when statistical parameters enter some almost sure synchronization region established by the developed approach. Moreover, some delicate configurations are considered on probability space for ensuring synchronization in networks whose nodes are described by nonlinear maps. Both theoretical and numerical results on synchronization are presented by setting only a few random connections in each switch duration. More interestingly, we analytically find it possible to achieve almost sure synchronization in the randomly switching complex networks even with very large population sizes, which cannot be easily realized in non-switching but deterministically connected networks.
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Affiliation(s)
- Yao Guo
- School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China
| | - Wei Lin
- School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China
| | - Daniel W C Ho
- Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Hong Kong, China
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Sun Y, Lin W. A positive role of multiplicative noise on the emergence of flocking in a stochastic Cucker-Smale system. CHAOS (WOODBURY, N.Y.) 2015; 25:083118. [PMID: 26328569 DOI: 10.1063/1.4929496] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In this article, we investigate the flocking of a stochastic Cucker-Smale system with multiplicative measurement noise. We show that there is a noise strength, below which the flocking occurs and the convergence time is a decreasing function of noise strength. Specifically, we find a power-law relationship between the convergence time and the density of group. We also investigate the influence of control parameter and an optimal value is found that minimizes the convergence time.
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Affiliation(s)
- Yongzheng Sun
- School of Science, China University of Mining and Technology, Xuzhou 221008, People's Republic of China
| | - Wei Lin
- School of Mathematical Sciences, LMNS, and Shanghai Key Laboratory of Data Science, Fudan University, Shanghai 200433, People's Republic of China
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10
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Sun Y, Li W, Zhao D. Convergence time and speed of multi-agent systems in noisy environments. CHAOS (WOODBURY, N.Y.) 2012; 22:043126. [PMID: 23278061 DOI: 10.1063/1.4768663] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
In this paper, the finite-time consensus problem of noise-perturbed multi-agent systems with fixed and switching undirected topologies is investigated. A continuous non-Lipschitz protocol for realizing stochastic consensus in a finite time is proposed. Based on the finite-time stability theory of stochastic differential equations, sufficient conditions are obtained to ensure finite-time stochastic consensus of multi-agent systems. An analytical upper bound for the convergence time is given. The effects of control parameters and noise intensity on convergence speed and time are also analyzed. Furthermore, numerical examples are provided to illustrate the effectiveness of the theoretical results.
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Affiliation(s)
- Yongzheng Sun
- School of Sciences, China University of Mining and Technology, Xuzhou 221008, People's Republic of China.
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Sun Y, Zhao D. Effects of noise on the outer synchronization of two unidirectionally coupled complex dynamical networks. CHAOS (WOODBURY, N.Y.) 2012; 22:023131. [PMID: 22757538 DOI: 10.1063/1.4721997] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We study the effect of noise on the outer synchronization between two unidirectionally coupled complex networks and find analytically that outer synchronization could be achieved via white-noise-based coupling. It is also demonstrated that, if two networks have both conventional linear coupling and white-noise-based coupling, the critical deterministic coupling strength between two complex networks for synchronization transition decreases with an increase in the intensity of noise. We provide numerical results to illustrate the feasibility and effectiveness of the theoretical results.
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Affiliation(s)
- Yongzheng Sun
- School of Sciences, China University of Mining and Technology, Xuzhou 221008, People's Republic of China.
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Xiao Y, Tang S, Xu Y. Theoretical analysis of multiplicative-noise-induced complete synchronization in global coupled dynamical network. CHAOS (WOODBURY, N.Y.) 2012; 22:013110. [PMID: 22462986 DOI: 10.1063/1.3677253] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
In this paper, based on the theory of stochastic differential equation, we study the effect of noise on the synchronization of global coupled dynamical network, when noise presents in coupling term. The theoretical result shows that noise can really induce synchronization. To verify the theoretical result, Cellular Neural Network neural model and Rössler-like system are performed as numerical examples.
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Affiliation(s)
- Yuzhu Xiao
- Department of Mathematics and Information Science, Chang'an University, Xi'an 710086, People's Republic of China.
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Sun Y, Ruan J. Synchronization in coupled time-delayed systems with parameter mismatch and noise perturbation. CHAOS (WOODBURY, N.Y.) 2009; 19:043113. [PMID: 20059209 DOI: 10.1063/1.3262488] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
In this paper, a design of coupling and effective sufficient condition for stable complete synchronization and antisynchronization of a class of coupled time-delayed systems with parameter mismatch and noise perturbation are established. Based on the LaSalle-type invariance principle for stochastic differential equations, sufficient conditions guaranteeing complete synchronization and antisynchronization with constant time delay are developed. Also delay-dependent sufficient conditions for the case of time-varying delay are derived by using the Lyapunov approach for stochastic differential equations. Numerical examples fully support the analytical results.
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Affiliation(s)
- Yongzheng Sun
- School of Sciences, China University of Mining and Technology, Xuzhou 221008, People's Republic of China.
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Xia Y, Yang Z, Han M. Lag synchronization of unknown chaotic delayed Yang-Yang-type fuzzy neural networks with noise perturbation based on adaptive control and parameter identification. ACTA ACUST UNITED AC 2009; 20:1165-80. [PMID: 19497816 DOI: 10.1109/tnn.2009.2016842] [Citation(s) in RCA: 78] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
This paper considers the lag synchronization (LS) issue of unknown coupled chaotic delayed Yang-Yang-type fuzzy neural networks (YYFCNN) with noise perturbation. Separate research work has been published on the stability of fuzzy neural network and LS issue of unknown coupled chaotic neural networks, as well as its application in secure communication. However, there have not been any studies that integrate the two. Motivated by the achievements from both fields, we explored the benefits of integrating fuzzy logic theories into the study of LS problems and applied the findings to secure communication. Based on adaptive feedback control techniques and suitable parameter identification, several sufficient conditions are developed to guarantee the LS of coupled chaotic delayed YYFCNN with or without noise perturbation. The problem studied in this paper is more general in many aspects. Various problems studied extensively in the literature can be treated as special cases of the findings of this paper, such as complete synchronization (CS), effect of fuzzy logic, and noise perturbation. This paper presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed adaptive scheme. This research also demonstrates the effectiveness of application of the proposed adaptive feedback scheme in secure communication by comparing chaotic masking with fuzziness with some previous studies. Chaotic signal with fuzziness is more complex, which makes unmasking more difficult due to the added fuzzy logic.
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Affiliation(s)
- Yonghui Xia
- Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China.
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Xiao Y, Xu W, Li X, Tang S. The effect of noise on the complete synchronization of two bidirectionally coupled piecewise linear chaotic systems. CHAOS (WOODBURY, N.Y.) 2009; 19:013131. [PMID: 19334995 DOI: 10.1063/1.3080194] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
In this paper, we study the synchronization of two bidirectionally coupled piecewise linear chaotic systems when the coupling strength is disturbed by the common or different noise. Based on stochastic differential equation theory, we verify that the noise can really induce the occurrence of synchronization, and the sufficient conditions of synchronization with probability 1 are established. We also find that with the common noise it is easier to induce the synchronization than with different noise. Moreover, two examples are provided and some numerical simulations are performed to verify the theoretical results.
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Affiliation(s)
- Yuzhu Xiao
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, People's Republic of China.
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Lin W, Ma HF. Failure of parameter identification based on adaptive synchronization techniques. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:066212. [PMID: 17677345 DOI: 10.1103/physreve.75.066212] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2006] [Indexed: 05/16/2023]
Abstract
In this paper, several examples as well as their numerical simulations are provided to show some possible failures of parameter identification based on the so-called adaptive synchronization techniques. These failures might arise not only when the synchronized orbit produced by the driving system is designed to be either some kind of equilibrium or to be some kind of periodic orbit, but also when this orbit is deliberately designed to be chaotic. The reason for emergence of these failures is theoretically analyzed in the paper and the boundedness of all trajectories generated by the coupled systems is rigorously proved. Moreover, synchronization techniques are proposed to realize complete synchronization and unknown parameter identification in a class of systems where nonlinear terms are not globally Lipschitz. In addition, unknown parameter identification is studied in coupled systems with time delays.
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Affiliation(s)
- Wei Lin
- Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, Research Center for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai 200433, China.
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Chen Z, Lin W, Zhou J. Complete and generalized synchronization in a class of noise perturbed chaotic systems. CHAOS (WOODBURY, N.Y.) 2007; 17:023106. [PMID: 17614660 DOI: 10.1063/1.2718491] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
In the paper, in light of the LaSalle-type invariance principle for stochastic differential equations, chaos synchronization is investigated for a class of chaotic systems dissatisfying a globally Lipschitz condition with noise perturbation. Sufficient criteria for both complete synchronization and generalized synchronization are rigorously established and thus successfully applied to realize chaos synchronization in the coupled unified chaotic systems. Furthermore, concrete examples as well as their numerical simulations are provided to illustrate the possible application of the established criteria.
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Affiliation(s)
- Zhang Chen
- Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, Research Center for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
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Yu S, Lü J, Tang WKS, Chen G. A general multiscroll Lorenz system family and its realization via digital signal processors. CHAOS (WOODBURY, N.Y.) 2006; 16:033126. [PMID: 17014231 DOI: 10.1063/1.2336739] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
This paper proposes a general multiscroll Lorenz system family by introducing a novel parameterized nth-order polynomial transformation. Some basic dynamical behaviors of this general multiscroll Lorenz system family are then investigated, including bifurcations, maximum Lyapunov exponents, and parameters regions. Furthermore, the general multiscroll Lorenz attractors are physically verified by using digital signal processors.
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Affiliation(s)
- Simin Yu
- College of Automation, Guangdong University of Technology, Guangzhou 510090, People's Republic of China
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