Permanence and viability
Two concepts from the nonequilibrium theory in systems analysis are discussed. These are permanence and viability. Permanence is a property of a system of ordinary differential equations in \(R^ n\) or in the simplex \(S_ n\subset R^ n\) for which the state space is an unreachable repellor. A sufficient condition for permanence in form of an average Lyapunov function method is proposed. Viability is a property of differential inclusions (or control systems) which means that the trajectories lie in the interior of a prescribed compact set. Some possibilities for applications of these two concepts in ecology, biological evolution, economy, biomathematics and so on are presented.
scientific article; zbMATH DE number 4079292