Zhang, Xinan; Liang, Zhaojun; Chen, Lansun Predator-prey dynamics in two-patch environments. (Chinese. English summary) Zbl 0906.92033 Bull. Biomath. 1, No. 1, 19-24 (1997). 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 Keywords:strong persistence; patch; dispersal rate; predator-prey Lotka-Volterra model PDFBibTeX XMLCite \textit{X. Zhang} et al., Bull. Biomath. 1, No. 1, 19--24 (1997; Zbl 0906.92033)