Dynamic analysis of a harvested fractional-order biological system with its discretization. (November 2021)

• Record Type: Journal Article
• Authors: Al-Nassir, Sadiq
• Is Part Of: Chaos, solitons and fractals. Volume 152(2021)
• Publication Date: 2021-11
• Subjects: Fractional order derivative -- Discretezation -- Prey- predator system -- Optimal control -- Harvesting; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111308
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: The complexity of nature that can not be modeled by means of ordinary or partial differential equations. This paper aims to study the dynamics behavior of fractional-order prey-predator system and its discretization with harvesting on prey species. The logistic growth of prey species and Holling type III functional response are considered. The existence and the local stability of all equilibria of fractional-order system, as well as its discretization, are determined and investigated. Then the discrete model is extended to an optimal control problem to get an optimal harvesting policy. We use the discrete version of Pontryagin maximum principle to derive the characterization of the optimal harvesting control and the optimal corresponding state solution. Numerical simulations are given to illustrate the theoretical findings.