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G. Sivaganesh

Publications and source records attributed to G. Sivaganesh.

12 recordsLinked to original sources
arXiv2023

Emergence of chaotic hysteresis in a second-order non-autonomous chaotic circuit

The observation of hysteresis in the dynamics of a third-order autonomous chaotic system namely, the {\it{Chua's}} circuit has been reported recently \cite{Gomes2023}. In the present work, we make a detailed study on the emergence of dynamical hysteresis in a simple second-order non-autonomous chaotic system namely, the {\it{Murali-Lakshmanan-Chua }} (MLC) circuit. The experimental realization of chaotic hysteresis is further validated by numerical simulation and analytical solutions. The presence of chaotic hysteresis in a second-order non-autonomous electronic circuit is reported for the first time. Multistable regions are observed in the dynamics of MLC with constant bias.

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arXiv2020

Effect of optimal uncoupling in enhancing synchronization stability in coupled chaotic systems

In this paper, we report a novel approach for studying the effect of optimal uncoupling on the stability of synchronization in coupled chaotic systems. The clipping of phase space of the driven system having an orientation along the coordinate axes revealing the nature of coupling of the state variables of coupled systems is identified in certain coupled third-order chaotic systems. The stability of synchronization is studied through the {\emph{Master Stability Function}} (MSF). The optimal directions of implementing the clipping width to achieve stable synchronization is observed by studying the effectiveness of clipping fraction and the sufficient range of orientation to identify the optimal directions is reported. The functional work steps for identifying the optimal directions are presented and the synchronization of the response system with the drive within the clipped region of phase space for different orientations of clipping width are studied. The stability of synchronization for different orientations of clipping widths and the two-parameter bifurcation diagram indicating the negative valued MSF regions obtained for the optimal direction of clipping width are presented. The application of the method of optimal uncoupling in identifying the direction of implication of clipping width is discussed and the range of orientation over which the clipping width has to be varied is generalized.

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arXiv2019

Generalized analytical solutions for secure transmission of signals using a simple communication scheme with numerical and experimental confirmation

A novel explicit analytical solution is reported for the transmission and recovery of information signals using a simple communication scheme. Analytical solutions are obtained for the normalized state equations of coupled second-order chaotic transmitter and receiver systems embedding the information signal. The analytical solution of the difference system obtained from the state equations of the transmitter and receiver systems has been identified as a measure of the recovered information signal which is transmitted securely by chaotic masking. The analytical solutions are used to reveal the nature of synchronization and the enhancement of the amplitude of recovered information signal. The difference signal of the coupled state variables indicating the recovered information signal obtained through numerical simulations is presented to validate the analytical results. The electronic circuit experimental results are presented to confirm the analytical and numerical results of the communication scheme discussed.

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arXiv2019

Numerical studies on the synchronization of a network of mutually coupled simple chaotic systems

We present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of synchronization behavior. The chaotic attractors of the simple $2 \times 2$ matrix network exhibiting strange non-chaotic attractors in their synchronization dynamics for smaller values of the coupling strength is reported. Further, the existence of islands of unsynchronized and synchronized states of strange non-chaotic attractors for smaller values of coupling strength is observed. The process of complete synchronization observed in the network with all the systems exhibiting strange non-chaotic behavior is reported. The variation of the slope of the singular continuous spectra as a function of the coupling strength confirming the strange non-chaotic state of each of the system in the network is presented. The stability of complete synchronization observed in the network is studied using the Master Stability Function.

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arXiv2019

Enhancement of induced synchronization by transient uncoupling in coupled simple chaotic systems

In this paper, we report the enhanced stability of induced synchronization by transient uncoupling observed in certain unidirectionally coupled second-order chaotic systems. The stability of synchronization observed in the coupled systems subjected to transient uncoupling is analyzed using the {\emph{Master Stability Function}}. The existence of the coupled systems in stable synchronized states over a certain range of the clipping fraction of the driven system is identified. The enhanced stable synchronized states are obtained for fixed values of clipping fraction in certain second-order chaotic systems. The two-parameter bifurcation diagram indicating the parameter regions over which stable synchronization occurs is presented. The negative eigenvalue regions of the driven system enabling induced synchronization is studied for all the systems. The enhancement of synchronization through transient uncoupling observed in coupled second-order non-autonomous chaotic systems is reported in the literature for the first time.

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arXiv2018

Stability enhancement by induced synchronization using transient uncoupling in certain coupled chaotic systems

In this work, we report the enhanced stability of induced synchronization observed through transient uncoupling in a class of unidirectionally coupled identical chaotic systems. The phenomenon of transient uncoupling implies the clipping of the chaotic attractor of the driven system in a drive-driven scenario and making the coupling strength active over the clipped regions. The {\emph{Master Stability Function}} (MSF) is used to determine the stability of the synchronized states for a finite clipping fraction in unidirectionally coupled chaotic systems subjected to transient uncoupling for fixed values of coupling strength. The effectiveness of transient uncoupling is observed through the existence of negative regions in the MSF spectrum for larger values of coupling strength. Further the two-parameter bifurcation diagram indicating the regions of stable synchronization for different values of clipping fraction and coupling strength has been obtained. The effect of the symmetry of chaotic attractors in enhancing the stability of synchronized states of coupled chaotic systems subjected to transient uncoupling is studied.

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arXiv2018

A Complete Analytical Study on the Dynamics of Simple Chaotic Systems

We report in this paper a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical solutions proving the numerically observed chaotic phenomena such as antimonotonicity, period-doubling sequences, Feignbaum remerging have been presented. Further, the analytical solutions are used to obtain the basins of attraction, phase-portraits and Poincare maps for different chaotic systems. Experimentally observed chaotic attractors in some of the systems are presented to confirm the analytical results. The bifurcations and chaotic phenomena studied through explicit analytical solutions is reported in the literature for the first time.

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arXiv2017

Generalized analytical solutions and experimental confirmation of complete synchronization in a class of mutually-coupled simple nonlinear electronic circuits

In this paper, we present a novel explicit analytical solution for the normalized state equations of mutually-coupled simple chaotic systems. A generalized analytical solution is obtained for a class of simple nonlinear electronic circuits with two different nonlinear elements. The synchronization dynamics of the circuit systems were studied using the analytical solutions. the analytical results thus obtained have been validated through numerical simulation results. Further, we provide a sufficient condition for synchronization in mutually-coupled, second-order simple chaotic systems through an analysis on the eigenvalues of the difference system. The bifurcation of the eigenvalues of the difference system as functions of the coupling parameter in each of the piecewise-linear regions, revealing the existence of stable synchronized states is presented. The stability of synchronized states are studied using the {\emph{Master Stability Function}}. Finally, the electronic circuit experimental results confirming the phenomenon of complete synchronization in each of the circuit system is presented.

nlin.CD↗
arXiv2016

On the synchronization of coupled forced negative conductance circuits: A numerical study

In this paper, a numerical study on the complete synchronization phenomenon exhibited by coupled forced negative conductance circuits is presented. The nonlinear system exhibiting two types of chaotic attractors is studied for complete synchronization of the identical chaotic attractors through phase portraits under one type of coupling. The stability of the synchronized states is observed for different coupling schemes of the circuit variables through {\emph{Master Stability Function}}. The Conditional lyapunov exponents explaining the dynamical behaviour of the driven system is presented.

nlin.CD↗
arXiv2016

An Analytical Study on the Synchronization of Strange Non-Chaotic Attractors

In this paper we present an analytical study on the synchronization dynamics observed in unidirectionally-coupled quasiperiodically-forced systems that exhibit Strange Non-chaotic Attractors (SNA) in their dynamics. The SNA dynamics observed in the uncoupled system is studied analytically through phase portraits and poincare maps. A difference system is obtained by coupling the state equations of similar piecewise linear regions of the drive and response systems. The mechanism of synchronization of the coupled system is realized through the bifurcation of the eigenvalues in one of the piecewise linear regions of the difference system. The analytical solutions obtained for the normalized state equations in each piecewise linear region of the difference system has been used to explain the synchronization dynamics though phase portraits and timeseries analysis. The stability of the synchronized state is confirmed through the Master Stability Function. An explicit analytical solution explaining the synchronization of SNAs is reported in the literature for the first time.

nlin.CD↗
arXiv2015

Numerical and analytical studies on the complete synchronization of the variant of Murali-Lakshmanan-Chua circuits

In this paper we present numerical and analytical studies on the complete synchronization phenomena exhibited by unidirectionally coupled two variant of Murali-Lakshmanan-Chua circuits. The transition of the coupled system from an unsynchronized state to a state of complete synchronization under the influence of the coupling parameter is observed through phase portraits obtained numerically and analytically.

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