Nonlinear Control Technique for Hyperchaotic Complex Nonlinear Systems

Authors

Kholod M. Abualnaja Department of Mathematics, Umm Al-Qura University, P.O. Box 14949, Makkah, Kingdom of Saudi Arabia
Emad E. Mahmoud Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt\\ College of Applied Medical Sciences, Taif University, Turabah, Kingdom of Saudi Arabia

Hyperchaos, Synchronization, Nonlinear control, Error system, Lyapunov functions, Co

This work presents hyperchaos synchronization between two identical hyperchaotic systems by using nonlinear control

technique. This technique is applied to achieve chaos synchronization for two identical hyperchaotic complex Chen systems. The

idea of hyperchaos synchronization is to use the output of the drive system to control the response system so that the output of the

response system follows the output of the drive system asymptotically. Lyapunov functions are derived to prove that the error systems

are asymptotically stable. Expressions are derived for the control functions which are used to achieve chaos synchronization. Numerical

simulations show the validity of these expressions.

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