Memristor-based asymmetric extreme multistable hyperchaotic system with a line of equilibria, coexisting attractors, its implementation and nonlinear active-adaptive projective synchronisation

In this paper, flux controlled quadratic memductance-based extreme multistable novel 4D hyperchaotic system and its active-adaptive projective synchronisation control is proposed. The proposed memristor-based extreme multistable hyperchaotic system has unstable line of equilibria and coexisting attractors. Different tools such as phase plane, time series, Lyapunov exponents, Lyapunov spectrum, Lyapunov dimension, Poincare map and recurrence analysis are used to evidence the different dynamic behaviours of the proposed 4D extreme multistable hyperchaotic system. The system shows twisted leaf shaped unique Poincare behaviour. Bifurcation plot is used to show the extreme multistability and coexisting behaviour in the proposed hyperchaotic system. Further, a nonlinear active-adaptive control is designed for the projective synchronisation between the proposed hyperchaotic and unknown parameter-based extreme multistable hyperchaotic systems. Active-adaptive control laws are designed by using relevant state variables of both known and unknown parameter-based hyperchaotic systems and required adaptive estimation laws are designed for error convergence. The required global asymptotic stability is ensured via Lyapunov's theorem of stability. Simulation is presented in MATLAB environment to demonstrate the effective verification of the theoretical approach and the objectives are attained successfully. Finally, the hardware implementation of proposed hyperchaotic system is accomplished using NI-MyRIO 1900 processor.