Dynamical study of two predators and one prey system with fractional Fourier transform method

Owolabi, Kolade M.; Pindza, Edson; Davison, Matt

doi:10.1002/num.22205

Cited by 7 publications

(2 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fractional calculus has been described as the generalization of classical derivatives and integrals to fractional order types. The concept of fractional operators has been used to model a number of physical and real-life phenomena in applied physics, control system [15,31,32,34,39], economics and finance [6], mathematical ecology and epidemiology [14,29,35,37], underground water, hydrology [3-5, 13, 42], among several other processes.…”

Section: Introductionmentioning

confidence: 99%

Analysis and numerical simulation of cross reaction–diffusion systems with the Caputo–Fabrizio and Riesz operators

Owolabi

2021

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

The evolutionary dynamics of cross‐reaction–diffusion equations of predator–prey type are investigated in the sense of fractional operator. In the models, we replace the classical time and spatial derivatives with the Caputo–Fabrizio and Riesz fractional derivatives, respectively. The nature of the resulting problem (is nonlinear, nonlocal, and nonsingular) do not either admit a closed form solution, while in most cases the analytical solution is too involved to be useful. As a result, there is need to provide a reliable numerical scheme that can approximate these derivatives in time and space. Hence, we formulate an approximation scheme with second‐order convergence rate for the time‐Caputo–Fabrizio fractional operator of order 0 < α ≤ 1 and L1 formula for the Riesz fractional derivative of order 1 < β ≤ 2 in space. As a case study, we consider two examples of strongly coupled cross fractional reaction–diffusion systems describing the interaction between two individual species that prey on the other one. We examine the system for stability analysis and establish the condition for the occurrence of Turing instability. The complexity of the dynamics of time–space cross fractional reaction–diffusion systems is theoretically studied and numerically in one and two dimensions for some instances of fractional orders.

show abstract

Section: Introductionmentioning

confidence: 99%

Analysis and numerical simulation of cross reaction–diffusion systems with the Caputo–Fabrizio and Riesz operators

Owolabi

2021

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

show abstract

“…The modeling of systems with differential equations has been an important research topic. Owolabi et al (2018) studied the analytical and numerical solutions of a dynamical model comprising three species of systems using the fractional Fourier transform. Alliera and Amster (2018) used the topological degree theory and proved the existence of positive periodic solutions for a system of delay differential equations.…”

Section: Introductionmentioning

confidence: 99%

Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials

et al. 2020

View full text Add to dashboard Cite

This paper addresses the application of generalized polynomials for solving nonlinear systems of fractional-order partial differential equations with initial conditions. First, the solutions are expanded by means of generalized polynomials through an operational matrix. The unknown free coefficients and control parameters of the expansion with generalized polynomials are evaluated by means of an optimization process relating the nonlinear systems of fractionalorder partial differential equations with the initial conditions. Then, the Lagrange multipliers are adopted for converting the problem into a system of algebraic equations. The convergence of the proposed method is analyzed. Several prototype problems show the applicability of the algorithm. The approximations obtained by other techniques are also tested confirming the high accuracy and computational efficiency of the proposed approach.

show abstract

Optimal control strategies for a computer network under virus threat

Avcı

Soytürk²

2023

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

Dynamical study of two predators and one prey system with fractional Fourier transform method

Abstract: coexistence, exponential time differencing method, fractional Fourier transform, global and local stability, nonlinear, predator-prey model, reaction-diffusion systemNumer Methods Partial Differential Eq. 2017;1-23.wileyonlinelibrary.com/journal/num

Cited by 7 publications

References 52 publications

Analysis and numerical simulation of cross reaction–diffusion systems with the Caputo–Fabrizio and Riesz operators

Analysis and numerical simulation of cross reaction–diffusion systems with the Caputo–Fabrizio and Riesz operators

Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials

Optimal control strategies for a computer network under virus threat

Contact Info

Product

Resources

About