Introduction to Terminal Dynamics

This paper introduces terminal dynamics as a set of ordinary differential equat ions which does not possess a unique solut ion, 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 th e solut ion splits into two equally probable branches. This property introduces elements of stochasticit y th at are associated with th e random walk paradigm. A relationship is established between th e original dynamical model and the corresponding Fokker-Planck equation for probability density. A new type of attractor that represents a stochast ic process is described . The relevance of the terminal model to irreversibility in Newtonian dynamics and to chaos theory is discussed.