# American Institute of Mathematical Sciences

March  2020, 13(3): 823-834. doi: 10.3934/dcdss.2020047

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

 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

* Corresponding author: koladematthewowolabi@tdtu.edu.vn (K. M. Owolabi)

Received  April 2018 Revised  May 2018 Published  March 2019

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, 2020, 13 (3) : 823-834. 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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