Qualitative properties and bifurcations of discrete-time Bazykin–Berezovskaya predator–prey model

A.A.Elsadany; Qamar Din; S.M.Salman

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Qualitative properties and bifurcations of discrete-time Bazykin–Berezovskaya predator–prey model

Qualitative properties and bifurcations of discrete-time Bazykin–Berezovskaya predator–prey model

作者：

A.A.Elsadany Qamar Din S.M.Salman

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Bazykin-Berezovskaya

model

period-doubling

bifurcation

Niemark-Sacker

bifurcation

transcritical

bifurcation

Chaotic

dynamics

摘要：

The positive connection between the total individual fitness and population density is called the demographic Allee effect.A demographic Allee effect with a critical population size or density is strong Allee effect.In this paper,discrete counterpart of Bazykin–Berezovskaya predator–prey model is introduced with strong Allee effects.The steady states of the model,the existence and local stability are examined.Moreover,proposed discrete-time Bazykin–Berezovskaya predator–prey is obtained via implementation of piecewise constant method for differential equations.This model is compared with its continuous counterpart by applying higher-order implicit Runge–Kutta method(IRK)with very small step size.The comparison yields that discrete-time model has sensitive dependence on initial conditions.By implementing center manifold theorem and bifurcation theory,we derive the conditions under which the discrete-time model exhibits flip and Niemark–Sacker bifurcations.Moreover,numerical simulations are provided to validate the theoretical results.

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篇名	Qualitative properties and bifurcations of discrete-time Bazykin–Berezovskaya predator–prey model
来源期刊	生物数学学报:英文版	学科	数学
关键词	Bazykin-Berezovskaya model period-doubling bifurcation Niemark-Sacker bifurcation transcritical bifurcation Chaotic dynamics
年，卷（期）	2020,（6）	所属期刊栏目
研究方向		页码范围	23-51
页数	29页	分类号	O17
字数		语种
DOI