Dynamical analysis of a new 5D hyperchaotic system

Abstract

This paper reports a new five-dimensional (5D) autonomous hyperchaotic system that is obtained by introducing two linear controllers to the Rabinovich system. The dynamical behaviors, including the boundedness, dissipativity and invariance, existence and stability of nonzero equilibrium points are studied and analyzed. The existences of the hyperchaotic and chaotic attractors are numerically verified through analyzing phase trajectories, Lyapunov exponent spectrum, bifurcations and Poincaré maps. The results indicate that the new 5D Rabinovich system can exhibit rich and complex dynamical behaviors. Finally, the existence of Hopf bifurcation, the stability and expression of the Hopf bifurcation are investigated by using the normal form theory and symbolic computations. Some cases are employed to test and verify the theoretical results.