Global stability of a periodic Holling-Tanner predator-prey model
نویسندگان
چکیده
منابع مشابه
Global stability in a diffusive Holling-Tanner predator-prey model
A diffusive Holling–Tanner predator–prey model with no-flux boundary condition is considered, and it is proved that the unique constant equilibrium is globally asymptotically stable under a new simpler parameter condition. © 2011 Elsevier Ltd. All rights reserved.
متن کاملPositive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response
The dynamic relationship between the predator and the prey has long been and will continue to be one of the dominant themes in population dynamics due to its universal existence and importance in nature 1 . In order to precisely describe the real ecological interactions between species such asmite and spidermite, lynx and hare, and sparrow and sparrow hawk, described by Tanner 2 and Wollkind et...
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We analyze a delayed Holling-Tanner predator-prey system with ratio-dependent functional response. The local asymptotic stability and the existence of the Hopf bifurcation are investigated. Direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are studied by deriving the equation describing the flow on the center manifold. Finally, numerical simulations are p...
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and Applied Analysis 3 transformed into the following nondimensional form: dx dt x 1 − x t − τ1 − xy a1 bx c1y , dy dt y [ δ − β t − τ2 x t − τ2 ] , 1.4 where a1 a/K, c1 cr/α, δ s/r, β sh/α are the non-dimensional parameters and they are positive. The main purpose of this paper is to consider the effect of multiple delays on system 1.4 . The local stability of the positive equilibrium and the e...
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and Applied Analysis 3 replication: stripes, cold/hot spots-stripes coexistence, and cold/hot spots patterns. Without the Allee effect, Peng and Wang [29, 30] analyzed the global stability of the unique positive constant steady state and established some results for the existence and nonexistence of positive nonconstant steady states. Wang et al. [31] considered the Turing and Hopf bifurcations...
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ژورنال
عنوان ژورنال: Mathematical Methods in the Applied Sciences
سال: 2018
ISSN: 0170-4214
DOI: 10.1002/mma.4814