Conditions For Occurrence Of Chaos Research Articles

Chaotic dynamics of the vibro-impact system under bounded noise perturbation

In this paper, chaotic dynamics of the vibro-impact system under bounded noise excitation is investigated by an extended Melnikov method. Firstly, the Melnikov method in the deterministic vibro-impact system is extended to the stochastic case. Then, a typical stochastic Duffing vibro-impact system is given to application. The analytic conditions for occurrence of chaos are derived by using the random Melnikov process in the mean-square-value sense. In addition, the numerical simulations confirm the validity of analytic results. Also, the influences of interesting system parameters on the chaotic dynamics are discussed.

Synchronization of variable-order fractional financial system via active control method

AbstractIn this paper, we study the chaotic dynamics of a Variable-Order Fractional Financial System (VOFFS). The Variable-Order Fractional Derivative (VOFD) is defined in Caputo type. A necessary condition for occurrence of chaos in VOFFS is obtained. Numerical experiments on the dynamics of the VOFFS with various conditions are given. Based on them, it is shown that the VOFFS has complex dynamical behavior, and the occurrence of chaos depends on the choice of order function. Furthermore, the chaos synchronization of the VOFFS is studied via active control method. Numerical simulations demonstrate that the active control method is effective and simple for synchronizing the VOFFSs with commensurate or incommensurate order functions.

Controlling Chaos for Fractional Order Genesio-Tesi Chaotic System Using Prediction-based Feedback Control

This paper deals with designing a prediction-based feedback control scheme for the fractional order Genesio-Tesi chaotic system. Based on the stability condition for occurrence of chaos, chaos control of fractional-order Genesio-Tesi system is investigated, the control strategy is fulfilled by stabilizing unstable fixed points of fractional chaotic system when the trajectory near to the target. The stability of the control scheme is studied and the compute price is low. Numerical simulations are also provided to verify the rightness and effectiveness of the proposed control scheme.

Chaos in fractional-order Genesio–Tesi system and its synchronization

In this paper we study the chaotic dynamics of fractional-order Genesio–Tesi system. Theoretically, a necessary condition for occurrence of chaos is obtained. Numerical investigations on the dynamics of this system have been carried out and properties of the system have been analyzed by means of Lyapunov exponents. It is shown that in case of commensurate system the lowest order of fractional-order Genesio–Tesi system to yield chaos is 2.79. Further, chaos synchronization of fractional-order Genesio–Tesi system is investigated via two different control strategies. Active control and sliding mode control are proposed and the stability of the controllers are studied. Numerical simulations have been carried out to verify the effectiveness of controllers.