On Chaotic Synchronization in a Linear Array of Chua's Circuits

Белых, В. Н.; Verichev, N. N.; Kocarev, Ljupčo; Chua, Leon O.

doi:10.1142/s0218126693000356

Cited by 46 publications

(7 citation statements)

References 5 publications

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“…Chains and arrays consisted of a large number of nonlinear elements with regular, chaotic, or stochastic behavior are widely applied in mathematical modeling of physical, optical, and radio-electronic extended systems [179,204,205,[255][256][257][258][259][260][261][262][263][264][265], as well as of chemical and biological processes [217-219, 221, 222, 255, 266-271]. Spatially extended systems can be represented by continuous media usually described by differential equations in partial derivatives as well as by ensembles of interacting elements (oscillators, self-sustained oscillators, maps, etc.)…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics of Chaotic and Stochastic Systems

Anishchenko¹,

Astakhov²,

Neiman³

et al. 2006

Springer Series in Synergetics

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Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics of Chaotic and Stochastic Systems

Anishchenko¹,

Astakhov²,

Neiman³

et al. 2006

Springer Series in Synergetics

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“…The problem of synchronizing networks of chaotic systems has been previously considered by several authors and from different perspectives [5][6][7][8][9][10][11][12][13][14]. In general, a network of N (possibly non-identical) nodes is said to exhibit bounded synchronization if:…”

Section: Synchronization: Definition and Toolsmentioning

confidence: 99%

“…These systems are also known as complex networks [1][2][3], and their collective dynamics is often considered as a property emerging from their interactions. A particularly intriguing problem that has attracted much attention in the recent literature is to unfold the sophisticated relationship between the network structure and collective phenomena such as synchronization [5][6][7][8][9][10][11][12][13][14]. Several collective phenomena have been investigated in complex networks, including those related to synchronization and control.…”

Section: Introductionmentioning

confidence: 99%

“…Several collective phenomena have been investigated in complex networks, including those related to synchronization and control. A particularly intriguing problem that has attracted much attention in the recent literature is to unfold the sophisticated relationship between the network structure and collective phenomena such as synchronization [5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Modular experimental setup for real‐time analysis of emergent behavior in networks of Chua's circuits

Magistris

Bernardo

Manfredi

et al. 2015

Circuit Theory & Apps

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This paper describes the design, realization and use of an analogical, fully reconfigurable experimental setup to analyze the complex dynamics of networks of chaotic circuits. It reports details of the implementation and characterization of the setup, together with representative results, showing its flexibility and potential. The setup allows to choose arbitrarily the coupling strength and interconnection structure among the circuits, the type of link and to select the parameters of the node dynamics. It has a modular structure, and it can accommodate up to 32 nodes interconnected by at most 32 links. The collective dynamics of a relatively large set of different network structures and configurations has been investigated using the setup. Synchronization, pattern formation and other interesting collective phenomena were observed experimentally, their evidence being reported here as an illustration of the potential of the proposed setup. Complex networks with linear diffusive coupling functionAs discussed at the beginning of this section, a complex network is mostly defined by the interconnection structure among its elementary dynamical units. As commonly done in the literature, 1552 M. DE MAGISTRIS ET AL.Figure 6. An example of synchronized chaotic dynamics for the case of 16 nodes, ring topology: (a) v C1 traces; (b) state plane v C1 -v C2 for each node; (c) synchronization diagrams v C11 -v C1k .

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“…As such, these circuits have been used to test strategies for the synchronization of nonlinear circuits [8], [9], [26] and networks [3], [5], [27], [31]- [34]. They have been extensively studied from a theoretical, numerical and experimental point of view (see [12] and references therein).…”

Section: F a Representative Example: Chua's Circuitmentioning

confidence: 99%

Synchronization of Networks of Non-Identical Chua's Circuits: Analysis and Experiments

Magistris

Bernardo

Tucci³

et al. 2012

IEEE Trans. Circuits Syst. I

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This paper is concerned with the theoretical and ex-\ud perimental analysis of synchronization and pinning control of net-\ud works of non-identical Chua’s circuits. The design and implemen-\ud tation is presented of an appropriate setup to carry out experi-\ud ments on networks of these nonlinear circuits with easily recon-\ud ﬁgurable parameter values. Then, the theoretical expectations are\ud validated of the so-called Extended Master Stability Function ap-\ud proach to study the onset of synchronization in the presence of real\ud parameter mismatches between the circuits at the network nodes.\ud The validation is carried out both numerically and experimentally.\ud For the ﬁrst time, the EMSF is also used to investigate pinning syn-\ud chronization in a network of non-identical circuits where a master\ud node (or pinner) is used to drive the network dynamics towards\ud some desired synchronous evolution. The numerical and experi-\ud mental results conﬁrm the viability of the EMSF as an effective\ud analysis and design tool

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On Chaotic Synchronization in a Linear Array of Chua's Circuits

Abstract: In this paper sufficient conditions that each cell in a one-dimensional array of Chua's circuits has an identical and synchronized behavior are given.

Cited by 46 publications

References 5 publications

Nonlinear Dynamics of Chaotic and Stochastic Systems

Nonlinear Dynamics of Chaotic and Stochastic Systems

Modular experimental setup for real‐time analysis of emergent behavior in networks of Chua's circuits

Synchronization of Networks of Non-Identical Chua's Circuits: Analysis and Experiments

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