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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

A Prey-Predator Dynamics with Square Root Functional Responses and Strong Allee Effect

Journal of Applied Nonlinear Dynamics 8(3) (2019) 419--433 | DOI:10.5890/JAND.2019.09.006

D. Pal$^{1}$, S. Biswas$^{2}$, G. S. Mahapatra$^{3}$, G. P. Samanta$^{4}$

$^{1}$ Chandrahati Dilip Kumar High School (H.S.), Chandrahati, West Bengal, 712504, India

$^{2}$ Polba High School, Polba, Hooghly-712148, West Bengal, India

$^{3}$ Department of Mathematics, National Institute of Technology-Puducherry, Karaikal-609605, India

$^{4}$ Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India

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Abstract

The major aim of this paper is to study the dynamical behaviour of a prey-predator system where the prey exhibits herd behaviour. Positivity, boundedness, some extinction criteria, stability of equilibrium points are represented with some global results. Numerical computations are discussed to illustrate the analytical findings. The biological implications of analytical and numerical findings are represented. This work also has a direct bearing to the possibilities of developing conditions for ecological balance in nature and by elaborate study and analysis, it throws enough light on the scope of further work in this field.

Acknowledgments

The authors are grateful to the anonymous referees and Editors Albert C. J. Luo and J. A. Tenreiro Machado for their careful reading, valuable comments and helpful suggestions, which have helped them to improve the presentation of this work significantly.

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