Global dynamics of a ratio-dependent predator-prey system View Full Text


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Article Info

DATE

2001-09

AUTHORS

Dongmei Xiao, Shigui Ruan

ABSTRACT

Recently, ratio-dependent predator-prey systems have been regarded by some researchers to be more appropriate for predator-prey interactions where predation involves serious searching processes. However, such models have set up a challenging issue regarding their dynamics near the origin since these models are not well-defined there. In this paper, the qualitative behavior of a class of ratio-dependent predator-prey system at the origin in the interior of the first quadrant is studied. It is shown that the origin is indeed a critical point of higher order. There can exist numerous kinds of topological structures in a neighborhood of the origin including the parabolic orbits, the elliptic orbits, the hyperbolic orbits, and any combination of them. These structures have important implications for the global behavior of the model. Global qualitative analysis of the model depending on all parameters is carried out, and conditions of existence and non-existence of limit cycles for the model are given. Computer simulations are presented to illustrate the conclusions. More... »

PAGES

268-290

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s002850100097

DOI

http://dx.doi.org/10.1007/s002850100097

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1015178879

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/11681529


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