Analytical studies on the dynamics of higher-dimensional nonlinear circuit systems

Sivaganesh, G.; Srinivasan, K.; Arulgnanam, A.

doi:10.1007/s12043-022-02428-6

Cited by 7 publications

(2 citation statements)

References 39 publications

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“…The considered simple Sprott type nonlinearities help in validating the proposed approach. Analytical solutions for the state equations of second-order non-autonomous circuits with piecewise-linear elements exhibiting chaotic, strange non-chaotic and synchronization behavior have been reported recently [32][33][34][35][36]. The evolution of chaotic dynamics in second-order systems with different simple nonlinearities discussed in the present work is studied through explicit analytical solutions.…”

Section: Introductionmentioning

confidence: 89%

Energy computation and multistability in a class of second-order chaotic systems with simple nonlinearities: numerical, experimental and analytical results

Sivaganesh¹,

Srinivasan²,

Fozin³

et al. 2022

Phys. Scr.

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The present work is aimed at the design, implementation and analysis of generic new second-order non-autonomous chaotic systems with simple nonlinear functions that have algebraically simple representations in mathematical form. These systems involve simple second-order non-autonomous ordinary differential equations with different simple nonlinearities like $G(x) (= x^2, |x|, max(x)$ and $min(x))$. The present study deals with numerical simulation, experimental analog circuit simulation results to demonstrate the ordered and chaotic phenomena being exhibited by these systems. Of most interest the striking phenomenon of multistability is uncovered for certain nonlinearities. Coexisting attractors are harnessed through the offset boosting approach. Also, the Hamilton energy is established through the Helmholtz theorem. It is found that both methods can be exploited as a non-bifurcation approach in characterizing multistability in the model. Further, analytical solutions developed for systems with certain nonlinearities are presented and the chaotic behavior of the systems studied using the solutions validating the numerical and experimental results are reported.

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Section: Introductionmentioning

confidence: 89%

Energy computation and multistability in a class of second-order chaotic systems with simple nonlinearities: numerical, experimental and analytical results

Sivaganesh¹,

Srinivasan²,

Fozin³

et al. 2022

Phys. Scr.

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“…Chua's circuit is one of the most extensively studied chaotic circuits and has led to the experimental realization of stochastic resonance, chaotic synchronization, and control of chaos [9][10][11][12]. It is a piece-wise linear third-order autonomous system that has also been studied analytically [13]. Recent research has reported hysteresis behavior in Chua's circuit with a DC offset voltage [1].…”

Section: Introductionmentioning

confidence: 99%

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

Sivaganesh¹,

Srinivasan²,

Fozin³

et al. 2023

Preprint

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The observation of hysteresis in the dynamics of a third-order autonomous chaotic system namely, the Chua's circuit has been reported recently [1]. In the present work, we make a detailed study on the emergence of dynamical hysteresis in a simple secondorder non-autonomous chaotic system namely, the 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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Theoretical Investigations on the Multistability, Quasiperiodicity and Synchronization of the Driven Chua’s Circuit

Sivaganesh

Srinivasan

2023

Circuits Syst Signal Process

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Analytical studies on the dynamics of higher-dimensional nonlinear circuit systems

Cited by 7 publications

References 39 publications

Energy computation and multistability in a class of second-order chaotic systems with simple nonlinearities: numerical, experimental and analytical results

Energy computation and multistability in a class of second-order chaotic systems with simple nonlinearities: numerical, experimental and analytical results

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

Theoretical Investigations on the Multistability, Quasiperiodicity and Synchronization of the Driven Chua’s Circuit

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