We use the coincidence degree to establish new results on the existence and uniqueness of T -periodic solutions for a kind of Duffing equation with two deviating arguments of the form x ′′ + Cx(t) + g1(t, x(t− τ1(t))) + g2(t, x(t− τ2(t))) = p(t).

In this paper, we study a class of nonlinear Duffing equations with a deviating argument and establish some sufficient conditions for the existence of positive almost periodic solutions of the equation. These conditions are new and complement to previously known results.

The problem of the dual synchronization of two different fractional-order chaotic systems is studied. By a linear controller, we realize the dual synchronization of fractional-order chaotic systems. Finally, the proposed method is applied for dual synchronization of Van der Pol-Willis systems and Van der Pol-Duffing systems. The numerical simulation shows the accuracy of the theory.

A very simple method for synthesizing the inverse system of a non-linear non-autonomous circuit containing nullors is proposed. The main application of the procedure is the synchronization of chaos by the inverse system approach. This is illustrated with two examples: the synchronization of a Duffing circuit and a communication scheme by direct chaotic modulation using Chua’s circuit. ( 1998 Jo...

this paper presents a new control scheme for a class of nonlinear systems. in the proposed method, an adaptive neural network observer with rise feedback controller are applied to realize sensorless control scheme. this observer is tuned online and no exact information of nonlinear term of plant is required. so, this characteristic can compensate mismodeling phenomena. also, a new controller ca...

Rényi entropy and generalized complexity measures are used to describe the chaotic behaviour of dynamical systems. These measures are found to be sensitive to the fine details of the Rössler and the Duffing maps. They are good descriptors of chaotic behaviour. Periodic windows and the fractal character of the chaotic dynamics are nicely detected.