CHEMICAL REACTION SYSTEMS WITH A HOMOCLINIC BIFURCATION: AN INVERSE PROBLEM (International Journal of Food and Nutritional Sciences, 2022)
A framework for inverse problems is offered to build reaction systems with specified features. The framework includes the definition and analysis of kinetic transformations, which enable the mapping of any polynomial ordinary differential equation to the one that may be represented as a reaction network. The framework is applied to the design of certain bistable reaction systems in two and three dimensions that experience a supercritical homoclinic bifurcation, and the phase spaces' topology is examined.