Analysis of food chain mathematical model under fractal fractional Caputo derivative
Open Access
- 1 January 2022
- journal article
- research article
- Published by American Institute of Mathematical Sciences (AIMS) in Mathematical Biosciences and Engineering
- Vol. 20 (2), 2094-2109
- https://doi.org/10.3934/mbe.2023097
Abstract
In this article, the dynamical behavior of a complex food chain model under a fractal fractional Caputo (FFC) derivative is investigated. The dynamical population of the proposed model is categorized as prey populations, intermediate predators, and top predators. The top predators are subdivided into mature predators and immature predators. Using fixed point theory, we calculate the existence, uniqueness, and stability of the solution. We examined the possibility of obtaining new dynamical results with fractal-fractional derivatives in the Caputo sense and present the results for several non-integer orders. The fractional Adams-Bashforth iterative technique is used for an approximate solution of the proposed model. It is observed that the effects of the applied scheme are more valuable and can be implemented to study the dynamical behavior of many nonlinear mathematical models with a variety of fractional orders and fractal dimensions.Keywords
This publication has 32 references indexed in Scilit:
- A new numerical approximation of the fractal ordinary differential equationThe European Physical Journal Plus, 2018
- New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic modelsThe European Physical Journal Plus, 2017
- Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex systemChaos, Solitons, and Fractals, 2017
- Complex behaviour in four species food-web modelJournal of Biological Dynamics, 2012
- Coexistence of competing predators in a coral reef ecosystemNonlinear Analysis: Real World Applications, 2011
- Food webs are built up with nested subwebsEcology, 2010
- Incorporating cannibalism into an age-structured model for the Chilean hakeFisheries Research, 2006
- Gigantic cannibals driving a whole-lake trophic cascadeProceedings of the National Academy of Sciences of the United States of America, 2003
- Simple Rules for Interspecific Dominance in Systems with Exploitative and Apparent CompetitionThe American Naturalist, 1994
- Simple mathematical models for cannibalism: A critique and a new approachMathematical Biosciences, 1986