F.M. Moukam Kakmeni

Chaos control and duration time of a class of uncertain chaotic systems

This Letter presents a robust control scheme for a class of uncertain chaotic systems in the canonical form, with unknown nonlinearities. To cope with the uncertainties, we combine Lyapunov methodology with observer design. The proposed strategy comprises an exponential linearizing feedback and an uncertainty estimator. The developed control scheme allows chaos suppression. The advantage of this method over the existing results is that the control time is explicitly computed. Simulations studies are conducted to verify the effectiveness of the scheme.

Nonlinear response and suppression of chaos by weak harmonic perturbation inside a triple well Φ6-rayleigh oscillator combined to parametric excitations

The nonlinear response and suppression of chaos by weak harmonic perturbation inside a triple well Φ 6 -Rayleigh oscillator combined to parametric excitations is studied in this paper. The main attention is focused on the dynamical properties of local bifurcations as well as global bifurcations including homoclinic and heteroclinic bifurcations. The original oscillator is transformed to averaged equations using the method of harmonic balance to obtain periodic solutions. The response curves show the saddle-node bifurcation and the multi-stability phenomena. Based on the Melnikovs method, horseshoe chaos is found and its control is made by introducing an external periodic perturbation.

ADAPTIVE OBSERVER-BASED EXACT SYNCHRONIZATION OF MISMATCHED CHAOTIC SYSTEMS

This paper proposes an adaptive observer-based synchronization of continuous-time chaotic systems. Our method concerns any chaotic system that comprises uncertainties. Using the Lyapunov stability theory, we show that the synchronization of two coupled chaotic systems can be achieved by means of a linear coupling. A remarkable feature of the proposed approach is that it is robust with respect to noise and parameter mismatch. Numerical simulation of the Chuas circuit verifies the efficiency and effectiveness of the proposed adaptive synchronization scheme.

AN ADAPTIVE OBSERVER FOR CHAOS SYNCHRONIZATION OF A NONLINEAR ELECTRONIC CIRCUIT

This Letter studies adaptive chaos synchronization between two coupled nonlinear electrical circuits using a linear state feedback. A simple and yet easily applicable algorithm is derived for adaptive chaos synchronization based on the Lyapunov stability theory. An adaptive linear state feedback is derived such that the coupled systems are globally synchronized. Numerical simulations show the effectiveness of the proposed synchronization scheme. A Pspice simulation of the adaptive synchronization process is performed to confirm the numerical results.

CHAOS AND ROBUST ADAPTIVE SYNCHRONIZATION IN A NONLINEAR EMITTER–RECEIVER SYSTEM

This work studies transitions to chaos and adaptive synchronization of a nonlinear emitter–receiver system in a drive–response framework. Safe bifurcations and explosive bifurcations are observed. A robust adaptive observer-based response system is designed to synchronize the emitter–receiver system with unknown parameters and external disturbances. Lyapunov stability ensures global synchronization between the drive and response systems even if Lipschitz constants on functions matrices and bound on uncertainties are unknown. Computer simulations are provided to illustrate the designed adaptive synchronization scheme.