@article{dc449b5d0c4e41a8aecb8838b9213a8e,
title = "Tristable Phenomenon in a Predator-Prey System Arising from Multiple Limit Cycles Bifurcation",
abstract = "In this paper, we consider a predator-prey system with Holling type III ratio-dependent functional response. Such a system can exhibit complex dynamical behavior such as bistable and tristable phenomena which contain equilibria and oscillating motions for certain parameter values. In particular, we show that the ratio-dependent predator-prey system can exhibit multiple limit cycles due to Hopf bifurcation, giving rise to coexistence of stable equilibria and stable periodic solutions. These solutions may reveal some new type of patterns of complex dynamical behaviors in predator-prey systems. ",
keywords = "Holling type functional response, Hopf bifurcation, Predator-prey system, bistable, tristable, focus value, limit cycle, normal form",
author = "Jiao Jiang and Wenjing Zhang and Pei Yu",
note = "Funding Information: This research was partially supported by the National Natural Science Foundation of China (No. 11201294), the Innovation Program of Shanghai Funding Information: Municipal Education Commission (No. 14YZ114), and the Natural Sciences and Engineering Research Council of Canada (No. R2686A02). Funding Information: This research was partially supported by the National Natural Science Foundation of China (No. 11201294), the Innovation Program of Shanghai Municipal Education Commission (No. 14YZ114), and the Natural Sciences and Engineering Research Council of Canada (No. R2686A02). Publisher Copyright: {\textcopyright} 2020 World Scientific Publishing Company.",
year = "2020",
month = jul,
day = "1",
doi = "10.1142/S0218127420501291",
language = "English",
volume = "30",
journal = "International Journal of Bifurcation and Chaos",
issn = "0218-1274",
number = "9",
}