Affiliation:
1. Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan
2. Mathematics Department, Faculty of Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia
Abstract
<abstract><p>In this paper, we explore the existence of fixed points, local dynamics at fixed points, bifurcations and chaos of a discrete prey-predator fishery model with harvesting. More specifically, it is proved that, for all involved parameters, the model has trivial fixed point, but it has semitrivial and interior fixed points under definite parametric condition(s). We study the local behavior at fixed points by applying the theory of linear stability. Furthermore, it is shown that flip bifurcation does not occur at semitrivial and trivial fixed points, but that the model undergoes Neimark-Sacker bifurcation at interior fixed point. It is also proved that, at interior fixed point, the model undergoes the flip bifurcation. By using a feedback control strategy, the chaos control is also examined. Finally, to illustrate the theoretical findings, detailed numerical simulations are provided.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference39 articles.
1. M. N. Huda, F. D. T. Amijaya, I. Purnamasari, The effect of harvesting activities on prey-predator fishery model with Holling type-Ⅱ in toxicant aquatic ecosystem, Aust. J. Math. Anal. Appl., 17 (2020), 13.
2. K. Pujaru, T. K. Kar, Impacts of predator-prey interaction on managing maximum sustainable yield and resilience, Nonlinear Anal., 25 (2020), 400–416. https://doi.org/10.15388/namc.2020.25.16657
3. T. K. Kar, Selective harvesting in a prey-predator fishery with time delay, Math. Comput. Modell., 38 (2003), 449–458. https://doi.org/10.1016/S0895-7177(03)90099-9
4. H. Liu, H. Yu, C. Dai, Z. Ma, Q. Wang, M. Zhao, Dynamical analysis of an aquatic amensalism model with non-selective harvesting and Allee effect, Math. Biosci. Eng., 18 (2021), 8857–8882. https://doi.org/10.3934/mbe.2021437
5. A. T. Keong, H. M. Safuan, K. Jacob, Dynamical behaviours of prey-predator fishery model with harvesting affected by toxic substances, Matematika, 34 (2018), 143–151. https://doi.org/10.11113/matematika.v34.n1.1018