Local Dynamics of a New Four-Dimensional Quadratic Autonomous System

Abstract

In this manuscript, Local dynamic behaviors including stability and Hopf bifurcation of a new four-dimensional quadratic autonomous system are studied both analytically and numerically. Determining conditions of equilibrium points on different parameters are derived. Next, the stability conditions are investigated by using Routh-Hurwitz criterion and bifurcation conditions are investigated by using Hopf bifurcation theory, respectively. It is found that Hopf bifurcation on the initial point is supercritical in this four-dimensional autonomous system. The theoretical results are verified by numerical simulation. Besides, the new four-dimensional autonomous system under the parametric conditions of hyperchaos is studied in detail. It is also found that the system can enter hyperchaos, first through Hopf bifurcation and then through periodic bifurcation.

Local Dynamics Analysis of a Four-Dimensional Hyperchaotic Lorenz System

“…The conditions guaranteeing the Hopf bifurcation were derived. Hu et al [4] studied stability and Hopf bifurcation of a new four-dimensional quadratic autonomous system both analytically and numerically. Aziz et al [5] designed a new electronic circuit as an engineering application on a four-dimensional chaotic system.…”