Self-Organized Patterns Induced by Neimark-Sacker, Flip and Turing Bifurcations in a Discrete Predator-Prey Model with Lesie-Gower Functional Response
Self-Organized Patterns Induced by Neimark-Sacker, Flip and Turing Bifurcations in a Discrete Predator-Prey Model with Lesie-Gower Functional Response
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DOI：
10.3390/e19060258
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发表时间：
2017-06
期刊：
影响因子：
2.7
通讯作者：
Feifan Zhang;Huayong Zhang;Shengnan Ma;T. Meng;Tousheng Huang;Hongju Yang
中科院分区：
文献类型：
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作者：
Feifan Zhang;Huayong Zhang;Shengnan Ma;T. Meng;Tousheng Huang;Hongju Yang
捕食者-食饵模型中自组织模式的形成一直是一个非常热门的话题。这些模型的动力学、分叉和斑图的形成是如此复杂，迫切需要研究。在本研究中，我们将一个具有Lesie-Gower功能性反应的连续捕食者-食饵模型转化为离散模型。对不动点和稳定性分析进行了研究。在稳定不动点附近，进行了包括Flip、Neimark-Sacker和Turing分叉的分叉分析，得到了分叉条件。基于这些分叉条件，选取参数值进行了方向图形成的数值模拟。模拟结果表明，Neimark-Sacker分叉产生了斑点、螺旋和从斑点到螺旋线的过渡图案。图灵分叉导致迷宫图案和螺旋与镶嵌图案的耦合，而翻转分叉导致许多不规则的复杂图案。与前人对具有Lesie-Gower功能反应的连续捕食-被捕食模型的研究相比，我们对离散模型的研究显示出更复杂的动力学和更多样的自组织模式。
The formation of self-organized patterns in predator-prey models has been a very hot topic recently. The dynamics of these models, bifurcations and pattern formations are so complex that studies are urgently needed. In this research, we transformed a continuous predator-prey model with Lesie-Gower functional response into a discrete model. Fixed points and stability analyses were studied. Around the stable fixed point, bifurcation analyses including: flip, Neimark-Sacker and Turing bifurcation were done and bifurcation conditions were obtained. Based on these bifurcation conditions, parameters values were selected to carry out numerical simulations on pattern formation. The simulation results showed that Neimark-Sacker bifurcation induced spots, spirals and transitional patterns from spots to spirals. Turing bifurcation induced labyrinth patterns and spirals coupled with mosaic patterns, while flip bifurcation induced many irregular complex patterns. Compared with former studies on continuous predator-prey model with Lesie-Gower functional response, our research on the discrete model demonstrated more complex dynamics and varieties of self-organized patterns.