Title: Further results on dynamical properties for a fractional-order predator-prey model

Authors: Yizhong Liu

Addresses: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550025, China

Abstract: On the basis of previous studies, we set up a new fractional-order predator-prey model. First, by basic theory of algebraic equation, we discuss the existence of equilibrium point. Second, with the help of Lipschitz condition, we discuss the existence and uniqueness of solution. Third, applying the derivative theory of functions, we prove the non-negativity of solution. Fourth, using the inequality technique of fractional-order differential equations, we obtain the sufficient condition to ensure the uniformly boundedness of solution. Fifth, by analysing the Jacobian matrix, the locally asymptotically stability of the equilibria has been investigated; By constructing some suitable Lyapunov functions, the globally asymptotically stability of the equilibria bas been analysed. Sixth, the computer simulation diagrams are displayed to illustrate the correctness of the analytic findings. Finally, a concise conclusion is give to end this paper.

Keywords: fractional-order predator-prey model; existence and uniqueness; non-negative; boundedness; stability; global asymptotic stability.

DOI: 10.1504/IJDSDE.2023.130302

International Journal of Dynamical Systems and Differential Equations, 2023 Vol.13 No.2, pp.108 - 127

Received: 15 Apr 2021
Received in revised form: 06 Apr 2022
Accepted: 19 Apr 2022
Published online: 17 Apr 2023 *

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