捕食者种群中具有自食和疾病的生态流行病模型的模式形成研究
Pattern Formation Study of an Eco-epidemiological Model with Cannibalism and Disease in Predator Population
摘要：
具有同类相食和疾病的生态-流行病模型的模式形成分析在文献中探讨较少。因此，在此基础上，我们提出了一个扩散的生态流行病模型，并在模型系统中进行了模式形成分析。通过线性化和李雅普诺夫函数技术，得到了系统恒正稳态局部渐近稳定性和全局渐近稳定性的充分条件。利用Cauchy不等式和Poincaré不等式，得到了该系统非常数正解不存在的正平衡态的先验估计.利用勒雷-绍德尔度理论研究了非定常正平衡态的存在性.的扩散系数，这是负责的外观固定模式的重要性进行了观察。使用数值模拟完成图案形成。此外，同类相食和疾病的影响，观察所提出的模型系统的动力学。猎物和敏感捕食者的移动在格局形成中起着重要作用。这些运动导致静止和非静止图案。据观察，增量的易感捕食者的运动以及同类相食的攻击率转换非图灵模式的图灵模式。李雅普诺夫谱计算的量化稳定和不稳定的动态。由具有不稳定极限环的参数集得到的非图灵模式比平稳模式更有趣、更真实。得到了稳态和非稳态的非图灵模式。
英文摘要：
Pattern formation analysis of eco-epidemiological models with cannibalism and disease has been less explored in the literature. Therefore, motivated by this, we have proposed a diffusive eco-epidemiological model and performed pattern formation analysis in the model system. Sufficient conditions for local asymptotic stability and global asymptotic stability for the constant positive steady state are obtained by linearization and Lyapunov function technique. A priori estimate for the positive steady state is obtained for the nonexistence of the nonconstant positive solution using Cauchy and Poincaré inequality. The existence of the nonconstant positive steady states is studied using Leray-Schauder degree theory. The importance of the diffusive coefficients which are responsible for the appearance of stationary patterns is observed. Pattern formation is done using numerical simulation. Further, the effect of the cannibalism and disease are observed on the dynamics of the proposed model system. The movements of prey and susceptible predator plays a significant role in pattern formation. These movements cause stationary and non-stationary patterns. It is observed that an increment in the movement of the susceptible predator as well as cannibalistic attack rate converts non-Turing patterns to Turing patterns. Lyapunov spectrum is calculated for quantification of stable and unstable dynamics. Non-Turing patterns obtained with parameter set having unstable limit cycle are more interesting and realistic than stationary patterns. Stationary and non-stationary non-Turing patterns are obtained.
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