title: Spatial Patterns of a Predator-Prey System of Leslie Type with Time Delay.
abstract: Time delay due to maturation time, capturing time or other reasons widely exists in biological systems. In this paper, a predator-prey system of Leslie type with diffusion and time delay is studied based on mathematical analysis and numerical simulations. Conditions for both delay induced and diffusion induced Turing instability are obtained by using bifurcation theory. Furthermore, a series of numerical simulations are performed to illustrate the spatial patterns, which reveal the information of density changes of both prey and predator populations. The obtained results show that the interaction between diffusion and time delay may give rise to rich dynamics in ecosystems.
authors.affiliation: Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000, Shan'xi, China.
authors.forename: Caiyun
authors.initials: C
authors.lastname: Wang
authors.affiliation: Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, China.
authors.forename: Lili
authors.initials: L
authors.lastname: Chang
authors.affiliation: College of Material Science and Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, Shan'xi, China.
authors.forename: Huifeng
authors.initials: H
authors.lastname: Liu
mesh_terms: D000818:Animals; D008954:Models, Biological; D011157:Population Dynamics; D011235:Predatory Behavior; D062206:Spatial Analysis; D013997:Time Factors