Spatial Patterns of a Predator-Prey System of Leslie Type with Time Delay

• Published in: PloS one Vol. 11; no. 3; p. e0150503
• Main Authors: Wang, Caiyun, Chang, Lili, Liu, Huifeng
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 01.03.2016; Public Library of Science (PLoS)
• Subjects: Analysis; Animals; Applied mathematics; Bifurcation theory; Biology and Life Sciences; Computer and Information Sciences; Computer simulation; Delay; Diffusion; Ecology and Environmental Sciences; Ecosystems; Environmental changes; Equilibrium; Growth rate; Mathematical analysis; Models, Biological; Numerical simulations; Pattern formation (Developmental biology); Physical Sciences; Population; Population Dynamics; Predation (Biology); Predator-prey simulation; Predatory Behavior; Prey; Spatial Analysis; Stability; Time Factors; Time lag; China
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0150503

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.