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

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.