Bifurcation analysis and chaos control in discrete chemical systems: Co-Dimension one and two insights from the Degn-Harrison model

Résumé fourni par la source

This research offers a well-developed analysis of the nonlinear dynamic behavior of a discrete-step Degn-Harrison system without diffusion. The continuous-time chemical reaction system is discretized by employing the explicit Euler scheme which results in a two-dimensional nonlinear map whose behavior depends on both the reaction parameters and the discretization step size. The presence and stability conditions of the interior equilibrium point are first established, and then the system’s bifurcation structure is explored in depth. Special attention is paid to codimension-one and codimension-two bifurcations, period-doubling, Neimark-Sacker and strong resonance cases (1:2, 1:3, and 1:4). To give a comprehensive characterization of these phenomena, we get the normal forms of these phenomena and check the non-degeneracy conditions of such phenomena, such that the validity of the theoretical results is ensured. Numerical simulations ensure the theoretical findings, such as bifurcation diagrams, phase portraits, and the maximum Lyapunov exponent, to give a picture of the switching from regular to chaotic dynamics. The outcomes of this study not only deepen the understanding of discretization-induced complexities in chemical kinetics as well as offering a structure for analyzing similar nonlinear systems within applied sciences.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.