Systems of differential equations that are competitive or cooperative. IV: Structural stability in three-dimensional systems. (English) Zbl 0734.34042

Summary: [For parts I-III see ibid. 13, 167-179 (1982; Zbl 0494.34017); ibid. 16, 423-439 (1985; Zbl 0658.34023); Nonlinearity 1, No.1, 51-71 (1988; Zbl 0658.34024); for part V see J. Differ. Equations 80, No.1, 94-106 (1989; Zbl 0712.34045).]
It is shown that among three-dimensional systems that are competitive or cooperative, those satisfying the generic Kupka-Smale conditions also satisfy the Morse-Smale conditions and are therefore structurally stable. This identifies a new and easily recognizable class of systems approximable by structurally stable systems.


34D30 Structural stability and analogous concepts of solutions to ordinary differential equations
37C10 Dynamics induced by flows and semiflows
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