Determination of Analytical Solution and Limit Cycle of Nonlinear Chemical Oscillations

Abstract

This work studies the determination of analytical solution and cycle limite in nonlinear chemical oscillations gouverned by a forced modified Van der Pol-Duffing oscillator. We considered the dynamic of nonlinear chemical systems subjected to an external sinusoidal excitation. The first order appoximative solution of the oxcillator is determined using the Lindstedt’sperturbation method. The limit cycle number of the oscillator is found as well as the effect of certain parameters of the model on cycle limit analyzes. The harmonic balance method is used to find the amplitudes of the oscillatory states. The effect of the constraint parameter β of the oscillator are observed on amplitude-response curves. Numerical simulations are used to validate the results obtained by analytical methods.