A new 4-D hyperchaotic Lü system with a curve equilibrium, its bifurcation analysis, multistability, circuit simulation and synchronization via integral sliding mode control

Abstract

In this research work, we first obtain a new 3-D chaotic Lü system by modifying the dynamics of the classical Lü chaotic system (2002). Next, by introducing a state feedback to the new 3-D modified Lü chaotic system, we obtain a new 4-D hyperchaotic Lü system with a curve equilibrium.We carry out a detailed bifurcation analysis of the new4-D hyperchaotic system with a curve equilibrium and describe the bifurcation transition diagrams and Lyapunov exponents diagrams.We also derive new multistability results of the new 4-D hyperchaotic Lü system with a curve equilibrium. For engineering applications, we provide an electronic circuit simulation of the proposed hyperchaotic Lü system using MultiSim 14.0. As a control application, we derive new results for the complete synchronization for a pair of new hyperchaotic Lü systems taken as the master and slave systems. We have used integral sliding mode control for the derivation of the synchronizing control law for the complete synchronization design for the new hyperchaotic Lü system. MATLAB simulations are provided to illustrate the main results of this research work.