The system stability of dynamic processes
The interest in this paper is in the system stability of the dynamic processes with multiple equilibria. Utilizing a no-cycle condition of \textit{J. S. Muldowney} [Rocky Mt. J. Math. 20, No. 4, 857-872 (1990; Zbl 0725.34049)] we derive two sufficient conditions for system stability, which provide generalizations of the dominant diagonal conditions with weights. The derived system stability conditions are, therefore, independent of adjustment coefficients. Our system stability conditions are applicable to various types of dynamic adjustment processes. We prove some properties concerning local stability and the number of stable equilibria. We also prove that almost any dynamical system which satisfies our system stability condition is Morse-Smale and, therefore, structurally stable.
dominant diagonal conditions with weights
scientific article; zbMATH DE number 1330494
scientific article