Complex Systems

Introduction to Terminal Dynamics Download PDF

Michail Zak
Jet Propulsion Laboratory, California Institute of Technology,
Pasadena, CA 91109


This paper introduces terminal dynamics as a set of ordinary differential equations which does not possess a unique solution, due to violation of the Lipschitz condition at equilibrium points. Each equilibrium point represents a terminal attractor that is approached in finite time or a terminal repeller for which the solution splits into two equally probable branches. This property introduces elements of stochasticity that are associated with the random walk paradigm. A relationship is established between the original dynamical model and the corresponding Fokker-Planck equation for probability density. A new type of attractor that represents a stochastic process is described. The relevance of the terminal model to irreversibility in Newtonian dynamics and to chaos theory is discussed.