Targeting and Control of Synchronization in Chaotic Oscillators (original) (raw)

Control of partial synchronization in chaotic oscillators

Pramana, 2015

A design of coupling is proposed to control partial synchronization in two chaotic oscillators in a driver-response mode. A control of synchrony between one response variables is made possible (a transition from a complete synchronization to antisynchronization via amplitude death and vice versa without loss of synchrony) keeping the other pairs of variables undisturbed in their pre-desired states of coherence. Further, one of the response variables can be controlled so as to follow the dynamics of an external signal (periodic or chaotic) while keeping the coherent status of other variables unchanged. The stability of synchronization is established using the Hurwitz matrix criterion. Numerical example of an ecological foodweb model is presented. The control scheme is demonstrated in an electronic circuit of the Sprott system.

Design of coupling for synchronization of chaotic oscillators

Physical Review E, 2009

A general procedure is discussed to formulate a coupling function capable of targeting desired responses such as synchronization, antisynchronization, and amplitude death in identical as well as mismatched chaotic oscillators. The coupling function is derived for unidirectional, mutual, and matrix type coupling. The matrix coupling, particularly, is able to induce synchronization, antisynchronization, and amplitude death simultaneously in different state variables of a response system. The applicability of the coupling is demonstrated in spiking-bursting Hindmarsh-Rose neuron model, Rössler oscillator, Lorenz system, Sprott system, and a double scroll system. We also report a scaling law that defines a process of transition to synchronization.

Engineering generalized synchronization in chaotic oscillators

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2011

We report a method of engineering generalized synchronization (GS) in chaotic oscillators using an open-plus-closed-loop coupling strategy. The coupling is defined in terms of a transformation matrix that maps a chaotic driver onto a response oscillator where the elements of the matrix can be arbitrarily chosen, and thereby allows a precise control of the GS state. We elaborate the scheme with several examples of transformation matrices. The elements of the transformation matrix are chosen as constants, time varying function, state variables of the driver, and state variables of another chaotic oscillator. Numerical results of GS in mismatched Rössler oscillators as well as nonidentical oscillators such as Rössler and Chen oscillators are presented. V

Targeting engineering synchronization in chaotic systems

International Journal of Modern Physics C, 2016

A method of targeting engineering synchronization states in two identical and mismatch chaotic systems is explained in detail. The method is proposed using linear feedback controller coupling for engineering synchronization such as mixed synchronization, linear and nonlinear generalized synchronization and targeting fixed point. The general form of coupling design to target any desire synchronization state under unidirectional coupling with the help of Lyapunov function stability theory is derived analytically. A scaling factor is introduced in the coupling definition to smooth control without any loss of synchrony. Numerical results are done on two mismatch Lorenz systems and two identical Sprott oscillators.

Adaptive mechanism for sync of chaotic oscillators

Abstract: This paper addresses the adaptive feedback controller design for synchronization of chaotic systems with interval time-delays in their state vectors by exploiting a lower and an upper bound on time-delays. Simple control and adaptation laws are developed for chaos synchronization and linear matrix inequalities (LMIs) are derived to ensure asymptotic convergence of the synchronization error between the master-slave systems, using the proposed feedback control strategy, by employing a novel treatment of Lyapunov-Krasovskii functional. Further, the proposed strategy is strengthened by exploiting 2 L stability against disturbances and perturbations and corresponding LMIs for robust adaptive controller synthesis are derived. Furthermore, a novel delay-range-dependent robust adaptive synchronization control approach for dealing with locally Lipschitz non-delayed and delayed nonlinearities in the dynamics of chaotic oscillators is provided by employing an additional adaptation law for the nonlinearities. A numerical simulation example is provided to illustrate effectiveness of the proposed synchronization approach.

Synchronization of Chaotic Oscillators With Partial Linear Feedback Control

arXiv: Chaotic Dynamics, 2019

We present a methodology for synchronization of chaotic oscillators with linear feedback control. The proposed method is based on analyzing the chaotic oscillator as a multi-mode linear system and deriving sufficient conditions for asymptotic stability. The oscillators are synchronized in a master-slave configuration, wherein a subset of the state variables for implementing the feedback control, enabling applications in cryptography for message encryption using the unused chaotic state variables. Controller stability is ensured through conventional root-locus technique for designing appropriate loop gain. We validate the methodology presented here with numerical simulations and experimental results obtained using an operational amplifier (op-amp) based electronic chaotic oscillator circuit.

Improved Time Response of Stabilization in Synchronization of Chaotic Oscillators Using Mathematica

Systems, 2016

Chaotic dynamics are an interesting topic in nonlinear science that has been intensively studied during the last three decades due to its wide availability. Motivated by much researches on synchronization, the authors of this study have improved the time response of stabilization when parametrically excited Φ 6-Van der Pol Oscillator (VDPO) and Φ 6-Duffing Oscillator (DO) are synchronized identically as well as non-identically (with each other) using the Linear Active Control (LAC) technique using Mathematica. Furthermore, the authors have synchronized the same pairs of the oscillators using a more robust synchronization with faster time response of stability called Robust Adaptive Sliding Mode Control (RASMC). A comparative study has been done between the previous results of Njah's work and our results based on Mathematica via LAC. The time response of stabilization of synchronization using RASMC has been discussed.

Designing Coupling for Synchronization and Amplification of Chaos

We propose a design of coupling for stable synchronization and antisynchronization in chaotic systems under parameter mismatch. The antisynchronization is independent of the specific symmetry (reflection symmetry, axial symmetry, or other) of a dynamical system. In the synchronization regimes, we achieve amplification (attenuation) of a chaotic driver in a response oscillator. Numerical examples of a Lorenz system, Rössler oscillator, and Sprott system are presented. Experimental evidence is shown using an electronic version of the Sprott system.

Generalized synchronization of chaotic oscillators

2006

The behavior of two unidirectionally coupled chaotic oscillators near the boundary of their generalized synchronization is analyzed. Using the modified system method, the position of this boundary on the plane of control parameters is considered and the physical mechanisms leading to the establishment of the generalized synchronization regime are elucidated.