Systemes dynamiques et Chaos

Abstract

Chaos, typical phenomenon of nonlinear systems, is now widely studied, because of its properties and many potential applications. Indeed, there may be chaos in many phenomena physical , chemical, meteorological, demographic or economic and its characteristics are that we can consider using it for application. In recent years, growing interests from engineering have stimulated the studies of chaos control , chaos synchronization , and chaos optimization Chaos is a kind of characteristics of nonlinear systems, which is a bounded unstable dynamic behavior that exhibits sensitive dependence on initial conditions and includes infinite unstable periodic motions. Although it appears to be stochastic, it occurs in a deterministic nonlinear system under deterministic conditions. The combination of optimization methods and fundamentals of chaotic systems are important issues in nonlinear science , has attracted interests from various fields in recent years and has received much attention in the literature. Chaotic optimization is a new stochastic optimization algorithm, which directly utilizes chaotic variables to search the optimal solution. The sensitive dependence on initial conditions and intrinsic stochastic property of chaos make chaotic optimization to obtain the global optimal solution more possible than the method having been adopted before. It can more easily escape from local minima than other stochastic algorithms. For this thesis, we seek original contributions on any aspect related to optimization methods with utilization of concepts of chaotic time series, attractors, Lyapunov exponents. These algorithms permitted to find with certitude a near neighborhood of the global optimum.