# American Institute of Mathematical Sciences

## Dynamical behaviour of fractional-order predator-prey system of Holling-type

 1 Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa 2 Department of Mathematical Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria

* Corresponding author: mkowolax@yahoo.com (K. M. Owolabi)

Received  April 2018 Revised  May 2018 Published  March 2019

Fund Project: The research contained in this report is supported by South African National Research Foundation

In this paper, the local derivative in time is replaced with the Caputo-Fabrizio fractional derivative of order $\alpha\in(0, 1)$. A two-step fractional version of the Adams-Bashforth method is formulated for the approximation of this derivative. To enhance the correct choice of parameters when numerically simulating the full-system, we examine the stability analysis of the main equation. Two important examples are drawn to explore the dynamic richness of the predator-prey model with Holling type. Simulation results at different instances of $\alpha$ is in agreement with the theoretical findings.

Citation: Kolade M. Owolabi. Dynamical behaviour of fractional-order predator-prey system of Holling-type. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020047
##### References:

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##### References:
Dynamic behaviour of fractional system (16) with $\alpha = 0.50$. Other parameters are as fixed in (17)
Dynamic behaviour of fractional system (16) with α = 0:79. Other parameters are as fixed in (17).
Dynamic behaviour of fractional system (16) with $\alpha = 0.91$. Other parameters are as fixed in (17)
A strange attractor for dynamic system (16) with $\alpha = 0.48$
One-dimensional distribution of time-fractional reaction-diffusion system (19) for $\alpha = 0.11$
One-dimensional distribution of time-fractional reaction-diffusion system (18) for α = 0:25
One-dimensional distribution of time-fractional reaction-diffusion system (18) for α = 0:45
One-dimensional distribution of time-fractional reaction-diffusion system (18) for α = 0:79
One-dimensional distribution of time-fractional reaction-diffusion system (18) for α = 0:91
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