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Analysis of fractional fishery model with reserve area in the context of time-fractional order derivative
- Source :
- Chaos, Solitons & Fractals. 140:110200
- Publication Year :
- 2020
- Publisher :
- Elsevier BV, 2020.
-
Abstract
- The paper addresses the mathematical analysis of the fishery model in the context of the fractional derivative operator. We use the Caputo–Fabrizio derivative in the investigations. We first prove the fishery model is biologically well definite by proposing the existence and the uniqueness of its solution. The main objective of this paper is to study the dynamics of the predator and the prey in the fishery model when the fractional-order derivative is used. Notably, we analyze the impact of the fractional-order derivative on the dynamics of the fishery model explicitly. To answer this issue, we introduce a new numerical scheme based on the discretization of the fractional integral associated with the Caputo–Fabrizio derivative. The numerical simulations of the solutions of the fractional model are intended to illustrate the numerical scheme presented in our paper. We finish by analyzing the local and global asymptotic stability of the equilibrium points using the Jacobian matrix and the Lyapunov direct method. The Lyapunov function is constructed using standard construction. We notice here that the solutions of the fractional fishery model with different values of the orders describes a cycle when we depict them in three dimensional spaces in time, and furthermore the marine reserves ensure the sustainability of fractional system.
- Subjects :
- Equilibrium point
Lyapunov function
Discretization
General Mathematics
Applied Mathematics
General Physics and Astronomy
Statistical and Nonlinear Physics
Context (language use)
01 natural sciences
010305 fluids & plasmas
Fractional calculus
Fishery
symbols.namesake
Exponential stability
0103 physical sciences
Jacobian matrix and determinant
symbols
Quantitative Biology::Populations and Evolution
Uniqueness
010301 acoustics
Mathematics
Subjects
Details
- ISSN :
- 09600779
- Volume :
- 140
- Database :
- OpenAIRE
- Journal :
- Chaos, Solitons & Fractals
- Accession number :
- edsair.doi...........ef0b0f677d2515df554e875bd2255360