Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

Jeevarekha, A; Asir, M. Paul; Philominathan, P.

doi:10.1142/s0218127416500942

Cited by 3 publications

(2 citation statements)

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“…Chaos has attracted appreciable attention due to its potential applications in weather forecasting, aircraft control, and secure communications [1]. Besides, nonlinear electronic circuits have been counted as powerful candidates in supplying experimental and analytical surveys for people to understand chaotic behaviors in these engineering applications.…”

Section: Introductionmentioning

confidence: 99%

“…Statistically speaking, most of the aforementioned memristive chaotic circuits can be regarded as two oscillating units coupled directly, linearly, or nonlinearly. Besides, an interesting work addresses the fact that two oscillators can share a common element to construct a chaotic circuit [1]. Inspired by these two considerations, a simple three-element-based memristive circuit including two memristors and one capacitor connected in parallel is presented, which can be regarded as two memristor-capacitor oscillating units with a sharing capacitor.…”

Section: Introductionmentioning

confidence: 99%

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Riddled Attraction Basin and Multistability in Three-Element-Based Memristive Circuit

Tan

Zhang

et al. 2020

Complexity

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By coupling a diode bridge-based second-order memristor and an active voltage-controlled memristor with a capacitor, a three-element-based memristive circuit is synthesized and its system model is then built. The boundedness of the three-element-based memristive circuit is theoretically proved by employing the contraction mapping principle. Besides, the stability distributions of equilibrium points are theoretically and numerically expounded in a 2D parameter plane. The results imply the memristive circuit has a zero unstable saddle focus and a pair of nonzero stable node-foci or unstable saddle-foci depending on the considered parameters. The dynamical behaviors include point attractor, period, chaos, coexisting bifurcation mode, period-doubling bifurcation route, and crisis scenarios, which are explored using some common dynamical methods. Of particular concern, riddled attraction basins and multistability are uncovered under two sets of specified model parameters nearing the tiny neighborhood of crisis scenarios by local attraction basins and phase plane plots. The riddled attraction basins with island-like structure demonstrate that their dynamical behaviors are extremely sensitive to the initial conditions, resulting in the coexistence of limit cycles with period-2 and period-6, as well as the coexistence of period-1 limit cycles and single-scroll chaotic attractors. Moreover, a feasible on-breadboard hardware circuit is manually made and the experimental measurements are executed, upon which phase plane trajectories for some discrete model parameters are captured to further confirm the numerically simulated ones.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%