Chua's Circuit: Control and Synchronization

Irimiciuc, Ștefan Andrei; Vasilovici, Ovidiu; Dimitriu, Dan Gheorghe

doi:10.1142/s0218127415500509

Cited by 5 publications

(1 citation statement)

References 23 publications

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“…Chua's circuit is a bridge to connect the characteristic associated to dynamics of nonlinear phenomena as: stable orbits, bifurcations or attractors, with the study of experimental chaos. This circuit, in its classic configuration, is one of the simplest chaotic systems containing an inductor, two capacitors which are the linear energy-storage elements, a linear resistor and one 2-terminal nonlinear resistor characterized by a current-voltage characteristic which has a negative slope [15]. All circuit elements are passive except for the nonlinear resistor; this element must be active in order for the circuit to become chaotic [7].…”

Section: Numerical Resultsmentioning

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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Section: Numerical Resultsmentioning

confidence: 99%