Potential Function in a Continuous Dissipative Chaotic System: Decomposition Scheme and Role of Strange Attractor

Abstract

We demonstrate, first in literature, that potential functions can be constructed in a continuous dissipative chaotic system and can be used to reveal its dynamical properties. To attain this aim, a Lorenz-like system is proposed and rigorously proved chaotic for exemplified analysis. We explicitly construct a potential function monotonically decreasing along the system's dynamics, revealing the structure of the chaotic strange attractor. The potential function is not unique for a deterministic system. We also decompose the dynamical system corresponding to a curl-free structure and a divergence-free structure, explaining for the different origins of chaotic attractor and strange attractor. Consequently, reasons for the existence of both chaotic nonstrange attractors and nonchaotic strange attractors are discussed within current decomposition framework.