A new 4-D hyperchaotic two-scroll system with two unstable equilibrium points, its dynamic analysis, circuit simulation and synchronization design via integral sliding mode control

Abstract

In this research work, a new hyperchaotic two-scroll system with two unstable equilibrium points has been derived and the qualitative properties of the new hyperchaotic system are detailed. A bifurcation analysis has been carried out for the proposed hyperchaotic two-scroll system by varying the system parameters. Multistability property of the new hyperchaotic two-scroll system has been also illustrated by showing the coexistence of hyperchaotic attractors for the proposed hyperchaotic two-scroll system for the same set of parameter values but different initial conditions. For engineering applications, we provide an electronic circuit simulation of the proposed hyperchaotic two-scroll system using MultiSim 14.0. As a control application, we derive new results for the complete synchronization for a pair of new hyperchaotic two-scroll systems taken as the master and slave systems. We have used integral sliding mode control and Lyapunov stability theory for the derivation of the synchronizing control law for the complete synchronization design for a pair of new hyperchaotic two-scroll systems. We have provided MATLAB simulations to illustrate and highlight the main results of this work.