Chaos synchronization is a procedure where one chaotic oscillator is forced to adjust the properties of another chaotic oscillator for all future states. This research paper studies and investigates the global chaos synchronization problem of two identical chaotic systems and two non‐identical chaotic systems using the linear active control technique. Based on the Lyapunov stability theory and using the linear active control technique, the stabilizing controllers are designed for asymptotically global stability of the closed‐loop system for both identical and non‐identical synchronization. Numerical simulations and graphs are imparted to justify the efficiency and effectiveness of the proposed scheme. All simulations have been done by using mathematica 9. © 2014 Wiley Periodicals, Inc. Complexity 21: 379–386, 2015

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Abstract-Controlling chaos is stabilizing one of the unstable periodic orbits either to its equilibrium point or to a stable periodic orbit by means of an appropriate continuous signal injected to the system. On the other hand, chaos synchronization refers to a procedure where two chaotic oscillators (either identical or nonidentical) adjust a given property of their motion to a common behavior. This research paper concerns itself with the Adaptive control and synchronization of a new chaotic system with unknown parameters. Based on the Lyapunov direct method (LDM), the Adaptive control techniques (ACTs) are designed in such a way that the trajectory of the new chaotic system is globally stabilized to one of its equilibrium points of the uncontrolled system. Moreover, the Adaptive control law is also applied to achieve the synchronization state of two identical systems and two different chaotic systems with fully unknown parameters. The parameters identification, chaos control and synchronization of the chaotic system have been carried out simultaneously by the Adaptive controller. All simulation results are carried out to corroborate the effectiveness and the robustness of the proposed methodology and possible feasibility for synchronizing two chaotic systems by using Mathematica 9.

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