Dynamics of stage-structured prey–predator model with prey refuge and harvesting

ABSTRACT

A stage-structured prey–predator model with prey refuge is assumed, where predators have two stages as immature and mature. We consider here the harvesting on prey only and analyze the model using Beddington-DeAngelis functional response. Local stability as well as global stability at an interior equilibrium point are investigated in the proposed model. We choose different types of bifurcation like Hopf bifurcation, saddle-node bifurcation, and transcritical bifurcation in the formulated model. Moreover, in this paper, we check the optimality of the harvesting function with the help of optimal control. We provide the numerical simulation of the proposed model for the confirmation of analytical results.

KEYWORDS:

• Stage-structure
• refuge
• harvesting
• Hopf bifurcation
• saddle-node bifurcation

Acknowledgments

The author, Aparna Das is very much grateful to the Council of Scientific and Industrial Research (CSIR) under Human Resource Development Group of India for providing financial support to continue this research work under Junior Research Fellowship (JRF) Scheme with CSIR Ref. No.: 18/12/2016(ii)EU-V dated 01.07.2017.

Disclosure statement

The authors do not have any possible conflicts of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Funding

This work was supported by the Council of Scientific and Industrial Research (CSIR) under Human Resource Development Group of India [CSIR: 18/12/2016(ii)EU-V dated 01.07.2017.].

Notes on contributors

Aparna Das

Sankar Kumar Roy obtained his MSc degree in Applied Mathematics from Vidyasagar University, Midnapore, India in 1996 and his PhD degree in Operations Research from IIT, Kharagpur, India in 2003. Presently he is working as a Full Professor in the Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India. His main research areas are Transportation Problem, Game Theory, Lattice in Discrete Mathematics, Fuzzy, Rough and Soft Set Theory, Stochastic Programming, Interval Programming, Multi-Choice Programming, Inventory Management and Bio-Mathematics. He is a senior member of International Economics Development Research Center (IEDRC), Hong Kong; member of International Journal of Development and Sustainability (IJDS), Japan. He is also Life Member of Calcutta Mathematical Society, Kolkata and Operational Research Society of India, Calcutta Chapter, Kolkata, West Bengal, India. He has to his credit several research papers published in International journals, including IEEE Transactions of Fuzzy Systems, Neural Computing and Applications, Applied Mathematical Modelling, Applied Intelligence, Annals of Operations Research, Mathematics and Computer in Simulation, International Journal of Uncertainty, Fuzzinessand Knowledge-Based Systems, Operational Research: An International Journal, international Journal of Computational Intelligence Systems, International Journal of Bio-Mathematics, International Journal of Bifurcation and Chaos, Water Resources Management, Computers and Industrial Engineering, Central European Journal of Operations Research, Journal of Industrial and Management Optimization, and Journal of Intelligent and Fuzzy Systems, many more.

Sankar Kumar Roy

Aparna Das is a Junior Research Scholar in the Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721102, West Bengal, India. She received her M. Sc. Degree in Mathematics from Gour Banga University West Bengal, India in 2015. Her main research interests on Mathematical Biology.