On The Synchronization of Van Der Pol-Duffing Oscillator

The most well known property of chaotic systems is their sensitivity to initial conditions. In this work the criterion presented in literature for synchronizing two chaotic systems is applied to a system consisting of two Van der Pol-Duffing oscillators. First, the route to chaos is investigated for the Duffing oscillator. Furthermore, the Lyapunov function approach is used to design a high dimensional chaotic system. Then certain subsystems of a nonlinear chaotic system are synchronized by linking them with a common signal. Synchronization has been observed when there exists an asymptotic stability and an appropriate Lyapunov function, also by computing all the Lyapunov exponents and Kolmogorov entropy.