Simulation and experimental implementations of memcapacitor based multi-stable chaotic oscillator and its dynamical analysis

Abstract

In this work, linear quadratic regulator (LQR) method is proposed for controlling and synchronizing memcapacitor based chaotic system (MMCO). The MMCO is constructed with a charge controller memcapacitor, a resistor, a conductance and two capacitors. The proposed oscillators dimensionless model is derived and considered for analysis. The investigations of the systems are made using nonlinear analyses tools such as bifurcation diagrams, Lyapunov exponents, phase portraits, bifurcation like sequence, time series and frequency spectra. To explore further on coexisting multiple attractors, we have also presented the basin of attraction for the MMCO. As the memcapacitor is not a commercially available component, we have to use a electronic circuit model simulation and realization for the complete dimensionless model of MMCO to confirm the hardware realizability. A LQR based chaos suppression and chaos synchronization algorithm is also proposed. For understanding active controller's impact on global asymptotic stability of synchronization and control errors, the Lyapunov function is used. Numerical analyses are demonstrated to reveal the effectiveness of applied active control method and the results are discussed.

Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator

“…In recent years, extreme multistability with the coexistence of infinitely many attractors [24][25][26][27][28] has attracted scientists' attention. This special phenomenon is frequently discovered in autonomous circuits and systems involving memory-circuit elements, since these circuits and systems have line or plane equilibrium sets [14,[29][30][31][32]. The stabilities of the equilibrium sets are determined by the initial conditions of memory-circuit elements, which induces the coexistence of infinitely many attractors.…”

A memristive chaotic system with two dimensional offset boosting and extreme multistability

“…A novel three-dimensional non-autonomous system exhibiting extreme and mega-stability was crafted by Sajad et al which demonstrated extreme sensitivity against variations in initial conditions about two distinct state variables [18]. Akif et al observed complex dynamical evolution in a chaotic oscillator, including multistability and chaos synchronization [19]. Lin et al apply a simplified multi-piecewise memristor to design a series of memristive multi-butterfly chaotic systems that can generate multi-butterfly chaotic attractors in one, two and three dimensions, respectively, and a change in the initial state of the memristor can also trigger initial offset boosting in three dimensions [20].…”

Dynamics of a simple third-order autonomous MLC circuit

“…In recent decades, the researches of chaos and its applications have been hot topics in the field of nonlinear dynamics [1][2][3]. The design of simple chaotic circuit plays a significant role in connecting the mathematical chaos to the physical world [4][5][6][7]. For the generation of chaos in electronic circuit, the nonlinear elements are indispensable.…”