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Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect

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  • Yongli Cai
  • Caidi Zhao
  • Weiming Wang

Abstract

We investigate a diffusive Leslie-Gower predator-prey model with the additive Allee effect on prey subject to the zero-flux boundary conditions. Some results of solutions to this model and its corresponding steady-state problem are shown. More precisely, we give the stability of the positive constant steady-state solution, the refined a priori estimates of positive solution, and the nonexistence and existence of the positive nonconstant solutions. We carry out the analytical study for two-dimensional system in detail and find out the certain conditions for Turing instability. Furthermore, we perform numerical simulations and show that the model exhibits a transition from stripe-spot mixtures growth to isolated spots and also to stripes. These results show that the impact of the Allee effect essentially increases the model spatiotemporal complexity.

Suggested Citation

  • Yongli Cai & Caidi Zhao & Weiming Wang, 2013. "Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-16, December.
    • Handle: RePEc:hin:jnljam:535746
    DOI: 10.1155/2013/535746
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    Cited by:

    1. Zhang, Huayong & Ma, Shengnan & Huang, Tousheng & Cong, Xuebing & Yang, Hongju & Zhang, Feifan, 2018. "A new finding on pattern self-organization along the route to chaos," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 118-130.
    2. Wang, Jinliang & Li, You & Zhong, Shihong & Hou, Xiaojie, 2019. "Analysis of bifurcation, chaos and pattern formation in a discrete time and space Gierer Meinhardt system," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 1-17.
    3. Huang, Tousheng & Zhang, Huayong, 2016. "Bifurcation, chaos and pattern formation in a space- and time-discrete predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 92-107.

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