Open AccessOn the existence of potential landscape in the evolution of complex systems
Author(s) -
Ao Ping,
Kwon Chulan,
Qian Hong
Publication year - 2007
Publication title -
complexity
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 61
eISSN - 1099-0526
pISSN - 1076-2787
DOI - 10.1002/cplx.20171
Subject(s) - symplectic geometry , invariant (physics) , transformation (genetics) , complex system , statistical physics , dynamical systems theory , computer science , pure mathematics , mathematics , algebra over a field , physics , artificial intelligence , mathematical physics , quantum mechanics , biology , biochemistry , gene
A recently developed treatment of stochastic processes leads to the construction of a potential landscape for the dynamical evolution of complex systems. Since the existence of a potential function in generic settings has been frequently questioned in literature, here we study several related theoretical issues that lie at core of the construction. We show that the novel treatment, via a transformation, is closely related to the symplectic structure that is central in many branches of theoretical physics. Using this insight, we demonstrate an invariant under the transformation. We further explicitly demonstrate, in one‐dimensional case, the contradistinction among the new treatment to those of Ito and Stratonovich, as well as others. Our results strongly suggest that the method from statistical physics can be useful in studying stochastic, complex systems in general. © 2007 Wiley Periodicals, Inc. Complexity 12: 19–27, 2007