Study of Dynamical Properties and Effective of a State u for Hyperchaotic Pan Systems

In this paper, we propose a new four-dimensional continuous autonomous hyperchaotic system which is built by adding a nonlinear controller to a three- dimensional chaotic Pan system. The new system is analyzed both theoretically and numerically by studying dynamical behaviors for this system, including equilibrium points, Lyapunov exponents, stability and bifurcation, also we study the stability, bifurcation andsymmetry for another four dimensional system which is generated by Pan in (2011) from the original system, we compared between two systems and found the difference between them. Finally, we show the effective of state u on the two systems.