Bifurcation Analysis of Solution for an Infinite System of Partial Differential Continuity Equations

This research focuses on the study of the bifurcation behavior of the solution for an Infinite System of Partial Differential Continuity Equations (ISPDCEs) appearing in the simulation of stochastic energy exchange between an Open Thermodynamic System (OTS) and incoming raw energy flow. Following the declared aim, ISPDCE reduces to a single randomized nonlinear differential equation. The closed-form solution obtained assumes the existence of the energy infrastructure in the form of two interconnected discrete energy families of admissible values. Analysis of the appropriate families reveals the key role of a phenomenon of symmetry breaking. The interconnected families are composed of the Points of Equilibrium (PoE) that are the placeholders for the energy bifurcations. The primary family is based on natural limitations imposed on the rate of energy exchange, while the secondary family is defined by the fundamental relation connecting the functionally dissimilar parts of the exchange energy. In this sense, the primary family creates the quantitative basis for the realization of the solution, whereas the secondary family presents an optimal way for the evolution of OTS marked by suitable bifurcations. Another important distinction of the secondary family is that it rails off by bifurcations in the energy area of constructive interaction of OTS with an energy flux and the remaining area with the nonevolutionary conditions.