Global Chaos Synchronization of the Forced Van der Pol Chaotic Oscillators via Adaptive Control Method

Chaos theory has a lot of applications in science and engineering. This paper first details the qualitative properties of the forced Van der Pol chaotic oscillator, which has important applications. Since its introduction in the 1920's, the Van der Pol equation has been a prototype model for systems with self-excited limit cycle oscillations. The Van der Pol equation has been studied over wide parameter regimes, from perturbations of harmonic motion to relaxation oscillations. It has been used by scientists to model a variety of physical and biological phenomena. Next, we derive new results for the global chaos synchronization of the identical forced Van der Pol chaotic oscillators via adaptive control method. MATLAB plots have been shown to illustrate the phase portraits of the forced Van der Pol chaotic oscillator and the adaptive synchronization of the forced Van der Pol chaotic oscillator.

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