Dynamics of Belousov Zhabotinsky Reaction Based Systems Via Nonlinear Stability Analyses

Controlling the dynamics of self-oscillating dynamical systems that are far from equilibrium has been a grand challenge for science and engineering. Belousov Zhabotinsky (BZ) reactions, a nonlinear chemical oscillator, has been used to design intrinsically powered self-oscillating dynamical systems. It has been known that the chemical oscillations in BZ reactions are due to the occurrence of Hopf bifurcation (HB). Here, reagent concentrations in the BZ system have been treated as the bifurcation parameter and we perform stability analyses to characterize the dynamics of the BZ system. Specifically, we calculate the first Lyapanov exponent to distinguish quantitatively between the subcritical and supercritical HB. In addition, we also calculate the second Lyapanov exponent to show that for a narrow range of bifurcation parameter, the sustained oscillations in the BZ system transforms in decayed oscillations with sensitive dependence on the initial condition. The transformation of this behavior occurs below a curve called Limit Point of Cycles which is a characteristic of Bautin bifurcation. The outcomes of our study can be utilized to characterize the behavior of dynamical systems and establish design rules for controlling their behavior.