Influence of the magnetic flux on the dynamics of a self-sustaining System: Analytical, numerical and analogical investigations

Abstract This paper investigates the nonlinear dynamics of a ferroelectric enzyme-substrate reaction modeled by \textcolor{red}{the} bi-rhythmic \emph{van der Pol} oscillator coupled to \textcolor{red}{the} magnetic flux. We derive the equilibrium points and study their stability. We analyze some bifurcation structures and the variation of the Lyapunov exponents. The phenomena of symmetric attractors and the anti-monotonicity are observed. \textcolor{red}{By} increasing the magnetic flux, \textcolor{red}{we find that the equilibrium points are stable}, tends to control chaotic regimes, and affects regular and quasi-regular ones. As the magnetic flux increases, the amplitude of the oscillations around the equilibrium points decreases and the \textcolor{red}{amplitude of the} limit cycles at the Hopf bifurcation \textcolor{red}{tends} to disappear. Further \textcolor{red}{increasing the magnetic flux gives} rise to chaotic dynamics. The electrical circuit and analogical simulations are \textcolor{red}{derived} using the PSpice software. \textcolor{red}{The agreement between analogical and numerical results is acceptable}.