Synchronization of nonlinearly coupled networks of Chua oscillators

Feketa, Petro; Schaum, Alexander; Meurer, Thomas; Michaelis, Dennis; Ochs, Karlheinz

doi:10.1016/j.ifacol.2019.12.032

Cited by 11 publications

(3 citation statements)

References 25 publications

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“…More basic chaotic maps, however, have serious security flaws. This shortcoming arises because of the restricted chaotic range, reduced chaotic complexity, and accelerated rate of degradation of dynamic behavior [32,33]. Several approaches for chaotic synchronization have been presented.…”

Section: Projective Synchronizationmentioning

confidence: 99%

Employing Quantum Fruit Fly Optimization Algorithm for Solving Three-Dimensional Chaotic Equations

2022

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In a chaotic system, deterministic, nonlinear, irregular, and initial-condition-sensitive features are desired. Due to its chaotic nature, it is difficult to quantify a chaotic system’s parameters. Parameter estimation is a major issue because it depends on the stability analysis of a chaotic system, and communication systems that are based on chaos make it difficult to give accurate estimates or a fast rate of convergence. Several nature-inspired metaheuristic algorithms have been used to estimate chaotic system parameters; however, many are unable to balance exploration and exploitation. The fruit fly optimization algorithm (FOA) is not only efficient in solving difficult optimization problems, but also simpler and easier to construct than other currently available population-based algorithms. In this study, the quantum fruit fly optimization algorithm (QFOA) was suggested to find the optimum values for chaotic parameters that would help algorithms converge faster and avoid the local optimum. The recommended technique used quantum theory probability and uncertainty to overcome the classic FA’s premature convergence and local optimum trapping. QFOA modifies the basic Newtonian-based search technique of FA by including a quantum behavior-based searching mechanism used to pinpoint the position of the fruit fly swarm. The suggested model has been assessed using a well-known Lorenz system with a specified set of parameter values and benchmarked signals. The results showed a considerable improvement in the accuracy of parameter estimates and better estimation power than state-of-the art parameter estimation approaches.

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Section: Projective Synchronizationmentioning

confidence: 99%

Employing Quantum Fruit Fly Optimization Algorithm for Solving Three-Dimensional Chaotic Equations

2022

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“…Our scenario, consider a master-slave nonidentical chaotic systems where the nonlinearities are represented by piecewise linear functions and we use as a example the Chua s equations [7]. These systems are simple electronic circuit that exhibits classic chaotic behavior and we will use them as representatives of a class of chaotic systems with nonlinearity given by piecewise linear functions [27,4,19] The solution to the synchronization problem mentioned above, in this case, begins with the selection of a linear coupling, although we believe that non-linear couplings [10] can be included in this same scheme, function. For this kind of coupling, several strategies have been proposed to achieve synchronization, see for instance [21].…”

Section: Introductionmentioning

confidence: 99%

Synchronization in a class of chaotic systems

J.¹,

Acosta²,

Garcia³

2021

Preprint

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In this work, the synchronization problem of a master-slave system of autonomous ordinary differential equations (ODEs) is considered. Here, the systems are, chaotic with a nonlinearity represented by a piecewise linear function, non-identical and linearly coupled.The idea behind our methodology is quite simple: we couple the systems with a linear function of the difference between the states of the systems and we propose a formal solution for the ODE that governs the evolution of that difference and then we determine what the parameters should be of the coupling function, so that the solution of that ODE is a fixed point close to zero.As the main result, we obtain conditions for the coupling function that guarantize the synchronization, based on a suitable descomposition of the system joined to a fixed point theorem.The scheme seems to be valid for a wide class of chaotic systems of great practical utility.

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“…Synchronization analysis of oscillatory networks is an active research topic having a variety of applications in neurophysiology (Cattai et al, 2019;Röhr et al, 2019;Menara et al, 2019c), distributed power generation (Balaguer et al, 2010) and power systems (Paganini and Mallada, 2019), secure communication and chaos (Argyris et al, 2005;Feketa et al, 2019a), memristive circuits (Ignatov et al, 2016(Ignatov et al, , 2017, biochemical networks (Scardovi et al, 2010), etc. A simple yet dynamically rich Kuramoto model proved to be an appropriate paradigm for synchronization phenomena (Acebrón et al, 2005;Dörfler and Bullo, 2014).…”

Section: Introductionmentioning

confidence: 99%

Stability of cluster formations in adaptive Kuramoto networks

Feketa¹,

Schaum²,

Meurer³

2020

Preprint

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This paper studies stability properties of multi-cluster formations in Kuramoto networks with adaptive coupling. Sufficient conditions for the local asymptotic stability of the corresponding synchronization invariant toroidal manifold are derived and formulated in terms of the intra-cluster interconnection topology and plasticity parameters of the adaptive couplings. The proposed sufficient stability conditions qualitatively mimic certain counterpart results for Kuramoto networks with static coupling which require sufficiently strong and dense intra-cluster connections and sufficiently weak and sparse inter-cluster ones. Remarkably, the existence of cluster formations depends on the interconnection structure between nodes belonging to different clusters and does not require any coupling links between nodes that form a cluster. On the other hand, the stability properties of clusters depend on the interconnection structure inside the clusters. This dependence constitutes the main contribution of the paper. Also, two numerical examples are provided to validate the proposed theoretical findings.

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Synchronization of nonlinearly coupled networks of Chua oscillators

Cited by 11 publications

References 25 publications

Employing Quantum Fruit Fly Optimization Algorithm for Solving Three-Dimensional Chaotic Equations

Employing Quantum Fruit Fly Optimization Algorithm for Solving Three-Dimensional Chaotic Equations

Synchronization in a class of chaotic systems

Stability of cluster formations in adaptive Kuramoto networks

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