title: Delay induced stability switch, multitype bistability and chaos in an intraguild predation model.
abstract: In many predator-prey models, delay has a destabilizing effect and induces oscillations; while in many competition models, delay does not induce oscillations. By analyzing a rather simple delayed intraguild predation model, which combines both the predator-prey relation and competition, we show that delay in intraguild predation models promotes very complex dynamics. The delay can induce stability switches exhibiting a destabilizing role as well as a stabilizing role. It is shown that three types of bistability are possible: one stable equilibrium coexists with another stable equilibrium (node-node bistability); one stable equilibrium coexists with a stable periodic solution (node-cycle bistability); one stable periodic solution coexists with another stable periodic solution (cycle-cycle bistability). Numerical simulations suggest that delay can also induce chaos in intraguild predation models.
authors: Department of Mathematics, Tongji University, Shanghai, 200092, P. R. China.
authors: Hongying
authors: H
authors: Shu
authors: Department of Mathematics and Statistics, University of New Brunswick, Fredericton, E3B 5A3, Canada.
authors: Xi
authors: X
authors: Hu
authors: Department of Mathematics and Statistics, University of New Brunswick, Fredericton, E3B 5A3, Canada. lwang2@unb.ca.
authors: Lin
authors: L
authors: Wang
authors: Department of Mathematics and Statistics, University of New Brunswick, Fredericton, E3B 5A3, Canada. watmough@unb.ca.
authors: James
authors: J
authors: Watmough
mesh_terms: D000818:Animals; D019295:Computational Biology; D017753:Ecosystem; D020387:Food Chain; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011235:Predatory Behavior
keywords: Bistability; Chaos; Intraguild predation; Stability switch; Time delay
references: Trends Ecol Evol. 1992 May;7(5):151-4
references: 21235990
references: Oecologia. 2005 Nov;146(1):110-9
references: 16041613
references: J Theor Biol. 2010 Jan 7;262(1):116-28
references: 19765596
references: J Math Biol. 2013 Nov;67(5):1227-59
references: 23001469
references: IMA J Math Appl Med Biol. 2001 Mar;18(1):41-52
references: 11339337
references: J Theor Biol. 2010 Jun 7;264(3):1033-42
references: 20223250
references: Ecology. 2011 Feb;92(2):352-61
references: 21618915
references: J Math Biol. 2014 Jan;68(1-2):477-503
references: 23306425
references: Oecologia. 2000 Oct;125(2):258-270
references: 24595837