Influence of the Magnetic Flux on the Dynamics of a self-sustained System: Analytical, numerical and analogical investigations

Abstract This paper investigates the nonlinear dynamics of a ferroelectric enzyme-substrate reaction modeled by a bi-rhythmic Van der Pol oscillator coupled to a magnetic flux. We derive the equilibrium points and study their stability, analyze some bifurcation structures and the variation of the corresponding Lyapunov exponents. The phenomena of symmetric attractors and the anti-monotonicity are observed. An increasing the magnetic flux stabilizes the equilibrium points, tends to control chaotic regimes, and affect regular and quasi-regular ones. As the magnetic flux increases, the amplitude of oscillations around the equilibrium point decreases and the limit cycles at the hopf bifurcation tend to disappear. Further increases the magnetic flux giving rise to chaotic dynamics. The electrical circuit and analogical simulations are performed using PSpice software. Analogical and numerical results agree.