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Heteroclinic cycles in ecological differential equations. (English) Zbl 0811.34035
The system of differential equations \(\dot x_ i = x_ i f_ i (x_ 1, \dots, x_ n)\) is supposed to have a heteroclinic cycle. Theorems, which guarantee asymptotic stability, instability, total instability of this cycle, are formulated in terms of a characteristic matrix with elements calculated by a local linearisation method. The proof is based on Lyapunov function technics. The paper generalizes many previous results concerning heteroclinic cycles.

MSC:
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
92D25 Population dynamics (general)
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