On the existence of potential landscape in the evolution of complex systems

Details On the existence of potential landscape in the evolution of complex systems On the existence of potential landscape in the evolution of complex systems

2007-03-20

arxiv.org/abs/q-bio/0703044v1

Complexity 12 (2007) 19-27

Biology

Quantitative Biology

Quantitative Methods

latex, 18 pages

Scientific paper

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,herewe study several related theoretical issues that lie at core of the construction. We showthat 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.

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