The complex dynamics of a diffusive prey–predator model with an Allee effect in prey

Rao, Feng; Kang, Yun

doi:10.1016/j.ecocom.2016.07.001

Cited by 38 publications

(26 citation statements)

References 55 publications

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“…In this research, we investigate a predatorprey system with Allee effect and Michaelis-Menten type functional response. Allee effect, which was introduced by as well as named after Allee, refers to a positive correlation between population density and the per capita growth rate [3,30]. Recently, Allee effect has been extensively explored to investigate its impact on dynamical features of predatorprey systems [12,13,15].…”

Section: Model Of the Spatiotemporal Discrete Predatorpreymentioning

confidence: 99%

“…Recently, Allee effect has been extensively explored to investigate its impact on dynamical features of predatorprey systems [12,13,15]. According to the research of Rao and Kang [3], the Michaelis-Menten type predator-prey system can exhibit great spatiotemporal complexity under the influence of Allee effect. Therefore, it holds significance and importance to further investigate the spatiotemporal Discrete Dynamics in Nature and Society 3 dynamics of the discrete form of such predator-prey system, which may show more complicated nonlinear characteristics.…”

Section: Model Of the Spatiotemporal Discrete Predatorpreymentioning

confidence: 99%

“…Many works have considered continuoustime models for the predator-prey systems with Allee effect. Numerical results in Rao and Kang [3] indicated that the spatial Michaelis-Menten type predation model with Allee effects exhibits rich dynamical transitions from wave growth not only to striped-like/spots patterns, but also to regular patterns, which implied that synergistic effects of diffusion and Allee effects can contribute to the patterns of the solutions in different ways. The dynamics of a reactiondiffusion predator-prey system with strong Allee effect in the prey population has been considered in Wang et al 's research [12], which revealed that the impact of Allee effect essentially increases the system spatiotemporal complexity.…”

Section: Introductionmentioning

confidence: 99%

“…To study the interactions between predator and prey in space, it is important to determine the specific forms of predator-prey functional response and spatial movement of the predator and prey populations [3]. Theoretically, there are a fair amount of works by using nonlinear reaction-diffusion equations to study the spatiotemporal dynamics of predatorprey systems [4,5].…”

Section: Introductionmentioning

confidence: 99%

“…Since the pioneering work of Lotka and Volterra on population dynamics [1,2], predator-prey relationship has become a central topic for biological studies over the last one hundred years because of its significance in many problems [3]. To study the interactions between predator and prey in space, it is important to determine the specific forms of predator-prey functional response and spatial movement of the predator and prey populations [3].…”

Section: Introductionmentioning

confidence: 99%

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Neimark-Sacker-Turing Instability and Pattern Formation in a Spatiotemporal Discrete Predator-Prey System with Allee Effect

Zhang

Cong

Huang

et al. 2018

Discrete Dynamics in Nature and Society

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A spatiotemporal discrete predator-prey system with Allee effect is investigated to learn its Neimark-Sacker-Turing instability and pattern formation. Based on the occurrence of stable homogeneous stationary states, conditions for Neimark-Sacker bifurcation and Turing instability are determined. Numerical simulations reveal that Neimark-Sacker bifurcation triggers a route to chaos, with the emergence of invariant closed curves, periodic orbits, and chaotic attractors. The occurrence of Turing instability on these three typical dynamical behaviors leads to the formation of heterogeneous patterns. Under the effects of Neimark-Sacker-Turing instability, pattern evolution process is sensitive to tiny changes of initial conditions, suggesting the occurrence of spatiotemporal chaos. With application of deterministic initial conditions, transient symmetrical patterns are observed, demonstrating that ordered structures can exist in chaotic processes. Moreover, when local kinetics of the system goes further on the route to chaos, the speed of symmetry breaking becomes faster, leading to more fragmented and more disordered patterns at the same evolution time. The rich spatiotemporal complexity provides new comprehension on predator-prey coexistence in the ways of spatiotemporal chaos.

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