Dynamics, Circuit Design and Synchronization of a New Five Equilibrium Hyperchaotic System

Based on a recently proposed chaotic finance system, a new four dimensional continuous time hyperchaotic system with five equilibrium points is constructed. It contains eleven terms with two quadratic and a quartic nonlinearities. First, major dynamical characteristics of this new system such as dissipativity, equilibrium points, Kaplan-York dimension, Lyapunov exponents spectrum and bifurcation diagrams are investigated analytically and numerically. After that, an electronic circuit is implemented using the Multisim software, which validates the feasibility of the proposed system. Numerical simulation and theoretical analysis show that the constructed system can exhibit periodic, chaotic and hyperchaotic behaviors, which is confirmed by circuit experiment. Finally, we have synchronized two identical new hyperchaotic systems with different initial conditions using active control.