Kybernetika

A four-dimensional hyperchaotic L\"{u} system with multiple time-delay controllers is considered in this paper. Based on the theory of Hopf bifurcation in delay system, we obtain a simple relationship between the parameters when the system has a periodic solution. Numerical simulations show that the assumption is a rational condition, choosing parameter in the determined region can control hyperchaotic L\"{u} system well, the chaotic state is transformed to the periodic orbit. Finally, we consider the differences between the analysis of the hyperchaotic Lorenz system, hyperchaotic Chen system and hyperchaotic L\"{u} system.