Dynamics of a predator–prey model with harvesting and reserve area for prey in the presence of competition and toxicity
- 140 Downloads
The aim of this paper is to present and study a three-dimensional continuous time dynamical system modeling a predator–prey with harvesting and reserve zone for the prey in the presence of competition and toxicity. We first prove that our model is ecologically and mathematically well-posed. In addition, the stability analysis is investigated by direct and indirect Lyapunov methods. By using the Pontryagin’s maximum principle, an optimal harvesting policy is established. Furthermore, numerical simulations are given in order to illustrate our theoretical results.
KeywordsPredator–prey model Competition Toxicity Stability Optimal harvesting policy
Mathematics Subject Classification34K18 34K20 92B20
- 1.Birkoff, G., Rota, G.C.: Ordinary Differential Equations. Ginn, Boston (1982)Google Scholar
- 9.Sabarmathi, A., Srinivas, M.N., Reddy, K.S., Das, K., Kumar, B.R.: Stability of a prey–predator fishery model with taxation & optimal harvesting policy. In: International Conference on Mathematical Computer Engineering (2013)Google Scholar
- 11.Toaha, S., Rustam, Z.: Optimal harvesting policy of predator-prey model with free fishing and reserve zones. In AIP Conference Proceedings 1825, 020023 (2017). https://doi.org/10.1063/1.4978992