STOCHASTICITY DEFINED EVOLUTION IN DYNAMICAL SYSTEMS AND COMPLEX NETWORKS

摘要

Nonlinear stochastic differential equations are often encountered in the quantitative modelling of phenomena in both natural and social sciences. One of the most important questions is the robustness and stability of the system. It is usually computationally expense to find it out by direct and real time calculation. Here we report a novel method allowing us to find a global measure of the stability without direct real time computation. It is similar to the finding of a "potential" in physical sciences. To be specific dynamics near and far from thermal equilibrium is studied within a new framework of stochastic differential equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in describing the system's evolution and destination. An explicit novel construction of the potential energy is illustrated through a gauged ψ-decomposition. Possible directions to extend the present study to generic situations are pointed out.