Abstract
The objective of this paper is to study the dynamics of the stochastic ratio-dependent predator–prey model with Holling III type functional response and nonlinear harvesting. For the autonomous system, sufficient conditions for globally positive solution and stochastic permanence are established. Then, applying comparison theorem for stochastic differential equation, sufficient conditions for extinction and persistence in the mean are obtained. In addition, we prove that there exists a unique stationary distribution and it has ergodicity under certain parametric restrictions. For the periodic system, we obtain conditions for the existence of a nontrivial positive periodic solution. Finally, numerical simulations are carried out to substantiate the analytical results.
Highlights
Renewable resources are considered to be inexhaustible at all times, but excessive exploitation will exhaust them
An adequate amount of thorough investigation is carried out to study the existence of periodic solutions for biological models with harvesting terms
Motivated by [1,2,3,4,5,6,7,8,9,10,11], in this paper, we propose the following ratio-dependent predator–prey system with Holling III type functional response and nonlinear harvesting terms, which is described as: dx(t) dt x(t)(r1
Summary
Renewable resources (such as fisheries and forestry resources) are considered to be inexhaustible at all times, but excessive exploitation will exhaust them. The harvesting effects on the dynamics of predator–prey systems have attracted lots of attention and considerable work has been done (see [3,4,5,6,7,8] and the references cited therein). In their papers, an adequate amount of thorough investigation is carried out to study the existence of periodic solutions for biological models with harvesting terms. Hou [4] discussed a ratio-dependent predator–prey system with
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