Large River Effect or Frozen Kinetics: How Complex Nonlinear Living Systems Solve Optimization Problems

In this paper, we introduce general idea of trajectories attraction in phase space, which is very common phenomenon for the processes in the Nature. We start from a rather general biological example of natural selection, where adaptation to the environmental conditions can be described as attraction of some population distribution in the phenotype space to a center of ecological niche. The niche is mathematically represented as the "survival coefficient" which in turn can be linked to a kind of energy potential. This link between biological and physical approaches may be very useful for solution of a wide range of biological problems. In particular, we discuss an evolution in complex potential with a lot of valleys in a multi-dimensional space accompanied by the so-called large river effect, which corresponds to an extremely slow evolution of some, normally close to final, stages of the adaptation. This effect is related to the practically important states of the "frozen kinetics" which accompanies extremely wide spectrum of phenomena and allows understanding different physical and biological processes.