Deterministic and stochastic analysis of a predator-prey model with Allee effect and herd behaviour

被引：11

作者：

Manna, Debasis ^{[1
]}

Maiti, Alakes ^{[2
]}

Samanta, G. P. ^{[3
]}

机构：

[1] Surendranath Evening Coll, Dept Math, Kolkata, W Bengal, India

[2] Vidyasagar Evening Coll, Dept Math, Kolkata, W Bengal, India

[3] Indian Inst Engn Sci & Technol, Dept Math, Sibpur 711103, Howrah, India

来源：

SIMULATION-TRANSACTIONS OF THE SOCIETY FOR MODELING AND SIMULATION INTERNATIONAL | 2019年 / 95卷 / 04期

关键词：

Prey-predator system; stability; herd; stochastic; Hopf bifurcation; ANIMAL AGGREGATIONS; LIMIT-CYCLES; DYNAMICS; DENSITY; GROWTH;

D O I：

10.1177/0037549718779445

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This paper aims to study the dynamics of a predator-prey model, where both prey and predator show herd behaviour. Due to this behaviour, predator-prey interaction occurs only at the outer edge of herds formed by the populations. Positivity and boundedness of the system are discussed. A criteria for the extinction of prey is established. A steady-state analysis has been performed. Some criteria for Hopf bifurcation are derived. The stochastic version of the model is formulated to take into account the effect of fluctuating environment. A criterion of asymptotic mean square stability of this model is derived. Numerical simulations are carried out to validate our analytical findings. Implications of our analytical and numerical findings are discussed critically.

引用

页码：339 / 349

页数：11

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