×

Predator-prey dynamics in two-patch environments. (Chinese. English summary) Zbl 0906.92033

Summary: This paper proves the following properties of a predator-prey Lotka-Volterra Model: All positive solutions are strongly persistent and the positive equilibrium (TPE) is stable as the dispersal rate is small; TPE is unstable as the dispersal rate is large and within an interval which bifurcates a unique, small-amplitude periodic solution; TPE is stable as the dispersal rate is larger than the supremum of the interval.

MSC:

92D40 Ecology
34C99 Qualitative theory for ordinary differential equations
34D99 Stability theory for ordinary differential equations
PDFBibTeX XMLCite