this paper introduces a technique for controlling a class of uncertain chaotic systems using an adaptive fuzzy proportional-integrator-derivative (pid) controller with h∞ tracking performance. the purpose of this work is to achieve optimal tracking performance of the controller using backtracking search algorithm (bsa). bsa, which is a novel heuristic algorithm, has an easy structure with singl...

In this article, we consider the nonlinear Duffing-van der Pol-type oscillator system by means of the first integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly, we apply the Division Theorem for two variables in the comple...

The Lyapunov based approach for synchronizing and identifying the unknown parameters in the Duffing system is presented in this paper. The strategy consists of proposing a slave system which has to follow asymptotically the desired Duffing system. The gains of the slave system are adjusted continually according to a convenient adaptation control law, until the measurable output error converges ...

Chaos theory has a manifold variety of applications in science and engineering. There are many systems in nature with several stable states, which are separated by energy barriers. When the system can move along the stable states, its dynamics can become quite complex. A simple mechanical model that depicts some of these complex dynamical features is the famous Duffing double-well oscillator (1...

A modified explicit hybrid method with four stages is presented, the first stage exactly integrating exp(wx), while remaining integrate sin(wx) and cos(wx). Special attention paid to phase properties of during process parameter selection. Numerical comparisons proposed existing methods for several second-order problems show that gives high accuracy in solving Duffing equation Kramarz’s system.

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...

We discuss a novel approach to control bifurcations in nonlinear systems. The aim of bifurcation tailoring is to design an appropriate control law such that the controlled system has a desired bifurcation diagram. After describing two open-loop bifurcation tailoring techniques, this paper proposes two alternative modified bifurcation tailoring methods based on the use of the Newton-flow algorit...

The nonlinear behavior analysis and chaos control for Duffing-Holmes chaotic system is discussed in the paper. In order to suppress the irregular chaotic motion, an optimal backstepping controller is designed. The backstepping method consists of parameters with positive values. The improper selection of the parameters leads to inappropriate responses or even may lead to instability of the syste...