Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 252-5258, Japan.
Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India.
Math Biosci Eng. 2019 May 1;16(5):3864-3884. doi: 10.3934/mbe.2019191.
We analyze the impact of aposematic time and searching efficiency of prey on the temporal and spatio-temporal dynamics of a diffusive prey-predator system. Here, our assumption is that the prey population primarily invests its total time in two activities-(i) defense against predation and (ii) searching for food, followed by growth-induced reproduction, whereas, predators do not involve in self-defense. Moreover, we consider that the reproduction rate of prey and the rate of predation have a negative linear correlation with the amount of time invested for aposematism. Based on the presump- tions, we find that unlike searching efficiency of prey, the aposematic time can diminish the proportion in which prey and predator coexist when it crosses a certain threshold, and at the extreme aposematism, the entire population drives into the extinction. The proposed dynamics undergoes Hopf-bifurcation with respect to the searching efficiency of prey. We examine the individual effect of aposematic time and searching efficiency on the formation of regular Turing patterns-the low to medium to high val-ues of defense-time and food searching efficiency generate 'spots' to 'stripes' to 'holes' pattern, re-spectively; however, the combined impact of both presents only non-Turing 'spot' pattern with the 'predominance of predators,' which happens through the Turing-Hopf bifurcation.
我们分析了警戒时间和猎物搜索效率对扩散型猎物-捕食者系统的时间和时空动态的影响。在这里，我们的假设是，猎物种群主要将其总时间投入到两项活动中——（i）防御捕食和（ii）寻找食物，然后进行生长诱导繁殖，而捕食者不参与自我防御。此外，我们认为猎物的繁殖率和捕食率与用于警戒的时间量呈负线性相关。基于这些假设，我们发现，与猎物的搜索效率不同，当警戒时间超过某个阈值时，它会减少猎物和捕食者共存的比例，而在极端警戒的情况下，整个种群都会灭绝。所提出的动力学对猎物的搜索效率存在 Hopf 分支。我们研究了警戒时间和搜索效率对规则图灵模式形成的个体影响——防御时间和食物搜索效率的低、中、高值分别产生“斑点”、“条纹”和“孔”模式；然而，两者的综合影响仅呈现非图灵“斑点”模式，即“捕食者优势”，这是通过图灵-霍普夫分支发生的。
