Pure and Applied Mathematics Quarterly

Volume 12 (2016)

Number 4

Globally asymptotical stability and existence of limit cycle for a generalized predator-prey model with prey refuge

Pages: 573 – 586

DOI: https://dx.doi.org/10.4310/PAMQ.2016.v12.n4.a6

Authors

Zhihui Ma (School of Mathematics and Statistics, Lanzhou University, Lanzhou, China)

Shufan Wang (School of Mathematics and Computer Science Institute, Northwest University for Nationalities, Lanzhou, China)

Tingting Wang (School of Mathematics and Statistics, Lanzhou University, Lanzhou, China)

Longheng Qian (Department of Mathematics and Economics, College of Letters and Science, University of California at Los Angeles)

Abstract

The stability property of the positive equilibrium and the existence of limit cycles for the Lotka–Volterra predator-prey system incorporating prey refuge with a generalized functional response are investigated. On the one hand, by constructing a suitable Lyapunov function and an auxiliary system, a new set of sufficient conditions which guarantee the global asymptotical stability of the positive equilibrium are obtained. On the other hand, a set of sufficient conditions which guarantee the existence of limit cycles are produced by modifying the theorem of Hesaaraki and Moghadas. Our results complement and supplement some known ones, and some published conclusions become the special cases of ours.

Keywords

predator-prey system, generalized response function, prey refuge, globally asymptotical stability, existence of limit cycle

Full Text (PDF format)

This work was supported by the National Natural Science Foundation of China (No. 11301238), the Fundamental Research Funds for the Central Universities (No. lzujbky-2017-166) and the Teaching Research Funds for Lanzhou University (No. 2017116).

Received 5 September 2016

Published 26 July 2018