Effects of passive hydrodynamics force on harmonic and chaotic oscillations in nonlinear chemical dynamics

Abstract This work studies the nonlinear dynamics and passive control of chemical oscillations governed by a forced modified Van der Pol–Duffing oscillator. We considered the dynamics of nonlinear chemical systems subjected to fluctuating hydrodynamic drag forces. The computation of fixed points of the nonlinear chemical system is made in detail by utilizing Cardan’s method. The harmonic balance method is used to find the amplitudes of the oscillatory states. The Floquet theory and the Whittaker method are utilized to analyze and analytically determine the stability boundaries of oscillations. The influences of system parameters in general and in particular the effect of the parameter K and the constraint parameter β which shows the difference between a nonlinear chemical dynamics order two differential equation and ordinary Van der Pol–Duffing equation are observed on the state of the second stability criterion. The effects of the control process on chaotic dynamics states are investigated through bifurcation structures, Lyapunov exponent, phase portraits and Poincare section. The results obtained by the analytical methods are validated and complemented by the results of numerical simulations.