Quantitative Biology

, Volume 1, Issue 1, pp 50–53

Stochastic physics, complex systems and biology


DOI: 10.1007/s40484-013-0002-6

Cite this article as:
Qian, H. Quant Biol (2013) 1: 50. doi:10.1007/s40484-013-0002-6


In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod’s necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated equilibria, spontaneous random “mutations” and “adaptations”. On an evolutionary time scale it produces sustainable diversity among individuals in a homogeneous population rather than convergence as usually predicted by a deterministic dynamics. The emergent discrete states in such a system, i.e., attractors, have natural robustness against both internal and external perturbations. Phenotypic states of a biological cell, a mesoscopic nonlinear stochastic open biochemical system, could be understood through such a perspective.

Copyright information

© Higher Education Press and Springer-Verlag GmbH 2013

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA

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