Adaptive control and synchronization of a new modified hyperchaotic Lü system with uncertain parameters

This paper addresses problems of control and synchronization for a new modified hyperchaotic Lü system with uncertain parameters. This new modified uncertain hyperchaotic Lü system is stabilized to its unique unstable equilibrium by using adaptive control. Furthermore, an adaptive control law and a parameter estimation update law are derived to synchronize two identical modified hyperchaotic Lü systems with uncertain parameters. Numerical examples are proposed to demonstrate and verify the theoretical analysis.