Abstract
In this paper, we consider a new fractional-order predator–prey model with Holling type-III functional response and stage structure. Based on the Lyapunov stability theory and by constructing a suitable Lyapunov functional, we obtain some sufficient conditions for the existence and uniqueness of positive solutions and the asymptotic stability of the positive equilibrium to the system. Finally, we give some numerical examples to illustrate the feasibility of our results.
Highlights
1 Introduction It is well known that the existence and uniqueness of positive solutions for predator–prey models with Holling type-III functional response and stage structure have been widely investigated by many researchers [1,2,3,4,5,6,7,8,9]
In [4], the authors studied the global properties of a predator–prey model with nonlinear functional response and stage structure for the predator, and the conditions of the existence and the global stability of the positive steady state were established
With the improvement of fractional calculus theory, the fractional differential equations are widely used in various fields, such as physics [17,18,19], economics [20,21,22], medicine [23, 24], and biology [25, 26], etc
Summary
It is well known that the existence and uniqueness of positive solutions for predator–prey models with Holling type-III functional response and stage structure have been widely investigated by many researchers [1,2,3,4,5,6,7,8,9]. To the best of our knowledge, up to now, few results are available for fractional-order predator–prey systems with Holling type-III functional response and stage structure It is a challenging and important problem in theory and applications. Motivated by the above discussion, in this paper, we consider the following fractionalorder predator–prey system with Holling type-III functional response and stage structure: dα x1 (t) dtα. Fractional-order predator–prey system with Holling type-III functional response and stage structure defined by modified fractional derivative is proposed.
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