By taking two-coupled duffing oscillator system as the research object, the study found under the synergistic effect of weak periodic signal and noise, the two-coupled duffing oscillator system has typical stochastic resonance and even could achieve better output of stochastic resonance than single duffing oscillator. Based on this phenomenon, this paper proposes a new method to detect the weak...

In this paper, a Fractional Adaptive Fuzzy Logic Control (FAFLC) strategy based on active fractional sliding mode (FSM) theory is considered to synchronize chaotic fractional-order systems. Takagi-Sugeno fuzzy systems are used to estimate the plant dynamics represented by unknown fractional order functions. One of the main contributions in this work is to combine an adaptive fractional order PI...

In this paper, the dynamic characteristics of fractional Duffing system are analyzed and studied by using improved short memory principle method. This method has small amount calculation high precision, can effectively improve problem large caused order. The influence frequency change on performance is nonlinear analysis methods, such as Phase Portrait, Poincare Map Bifurcation Diagram. Moreove...

A chaotic system is one whose long term behavior is unpredictable and is sensitive to the initial conditions. This thesis explores the idea of inducing chaos in systems as a means to render them inoperable. The idea is to use resonant external perturbations to drive nonlinear oscillators into progressively higher resonant states and eventually into chaos. The advantage of this approach over con...

We consider in this paper the dynamics and synchronization of coupled chaotic Van der PolDuffing systems. The stability of the synchronization process between two coupled autonomous Van der Pol model is first analyzed analytically and numerically, before following the problem of synchronizing chaos both on the same and different chaotic orbits of two coupled Van der Pol-Duffing systems. The sta...

Smale horseshoes, curvilinear rectangles and their U-shaped images patterned on Smale’s famous example, provide a rigorous way to study chaos in dynamical systems. The paper is devoted to constructing them in two-dimensional diffeomorphisms with the existence of transversal homoclinic saddles. We first propose an algorithm to automatically construct “horizontal” and “vertical” sides of the curv...