A single species model with impulsive diffusion and pulsed harvesting

In this paper, a single species model with impulsive diffusion between two patches is proposed, which provides a more natural description of plant seeds dynamics compared with the continuous or discrete ones. By using the discrete dynamical system generated by a monotone, concave map for the dispersal model and a ∊1 - ∊2 variation, it is proved that the Poincare map has a globally stable positive fixed point. This implies that the system considered here has a globally stable positive periodic solution under some sufficient conditions. Further numerical simulations show that the diffusion can save the extinction though the species has a negative growth rate in one patch.

Download Full-text

Impulsive diffusion in single species model

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2006.01.102 ◽

2007 ◽

Vol 33 (4) ◽

pp. 1213-1219 ◽

Cited By ~ 34

Author(s):

Limin Wang ◽

Zhijun Liu ◽

Jinghui ◽

Lansun Chen

Keyword(s):

Single Species ◽

Impulsive Diffusion ◽

Single Species Model

Download Full-text

Analysis of a Single Species Model with Dissymmetric Bidirectional Impulsive Diffusion and Dispersal Delay

Journal of Applied Mathematics ◽

10.1155/2014/701545 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11

Author(s):

Haiyun Wan ◽

Long Zhang ◽

Zhidong Teng

Keyword(s):

Population Dynamics ◽

Periodic Solution ◽

Global Stability ◽

Positive Periodic Solution ◽

Single Species ◽

Migration Behavior ◽

Natural Ecosystem ◽

Impulsive Diffusion ◽

Theoretical Results ◽

Single Species Model

In most models of population dynamics, diffusion between two patches is assumed to be either continuous or discrete, but in the real natural ecosystem, impulsive diffusion provides a more suitable manner to model the actual dispersal (or migration) behavior for many ecological species. In addition, the species not only requires some time to disperse or migrate among the patches but also has some possibility of loss during dispersal. In view of these facts, a single species model with dissymmetric bidirectional impulsive diffusion and dispersal delay is formulated. Criteria on the permanence and extinction of species are established. Furthermore, the realistic conditions for the existence, uniqueness, and the global stability of the positive periodic solution are obtained. Finally, numerical simulations and discussion are presented to illustrate our theoretical results.

Download Full-text