Coexistence of hyperchaos with chaos and its control in a diode-bridge memristor based MLC circuit with experimental validation

Abstract

This paper reports both the coexistence of chaos and hyperchaos and their control based on a noninvasive temporal feedback method for attractor selection in a multistable non-autonomous memristive Murali-Lakshamanan-Chua (MLC) system. Numerical simulation methods such as bifurcation diagrams, the spectrum of Lyapunov exponents, phase portraits, and cross-section basins of initial states are used to examine several striking dynamical features of the system, including torus, chaos, hyperchaos, and multistability. Of most interest, the rare phenomenon of the coexistence of hyperchaos and chaos has been uncovered based on bifurcation techniques and nonbifurcation scheme like offset boosting. Further analyses based on intermittent feedback-based control in the time domain help to drive the system from the multistable state to a monostable one where only the hyperchaotic attractor survives. Since the attractor's internal dynamics are retained, this control method is non-invasive. At the end of our analyses, the results of both PSpice and that of the microcontroller-based digital calculator of the circuit match perfectly with the numerical investigations.

Dynamical behavior analysis of the heart system by the bifurcation structures

“…The bifurcation diagram is a representation of the abscissa in the plane [ 58 , 59 ] where is a parameter of the differential system called control parameter when it is incremented. is the integration step.…”

“…To acquire the most information when study of a dynamic system is performed, its maximum Lyapunov exponent is generally analyzed [ 58 , 59 ]. It is a curve that shows a large number of dynamic behaviors that is not always known.…”

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

“…Offset boosting is an easy and reliable method to identify any coexisting dynamics in the phase space [22][23][24]. Offset boosted systems are obtained by introducing a constant vector into the state variables of an investigated system.…”

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

“…Such property as been worthy in tracking coexisting attractors with large or relatively small intermingled basin of attraction. Indeed, such approach includes easiness, reliability and vigilance [30]. Traditional methods exploited so far were related to bifurcation analysis which are time-consuming, complex and uncertain depending on the type of the system one deals with (i.e., hidden or self-excited).…”

“…It consists of exploiting the offset boosting property to shift any dynamic and related demarcation region of initial states in the phase plane. Apart from being less computational it is also found to be non-invasive [30,31]. The present work introduces another non-bifurcation approach based on the computed Hamilton energy for detecting multistabilty in nonlinear dynamical system.…”