Raw S N, Mishra P, Sarangi B P, Tiwari B
Department of Mathematics, National Institute of Technology Raipur, Raipur, Chhattisgarh 492010 India.
Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland.
Iran J Sci Technol Trans A Sci. 2021;45(4):1417-1436. doi: 10.1007/s40995-021-01139-8. Epub 2021 May 7.
The ecological theory of species interactions rests largely on the competition, interference, and predator-prey models. In this paper, we propose and investigate a three-species predator-prey model to inspect the mutual interference between predators. We analyze boundedness and Kolmogorov conditions for the non-spatial model. The dynamical behavior of the system is analyzed by stability and Hopf bifurcation analysis. The Turing instability criteria for the Spatio-temporal system is estimated. In the numerical simulation, phase portrait with time evolution diagrams shows periodic and chaotic oscillations. Bifurcation diagrams show the very rich and complex dynamical behavior of the non-spatial model. We calculate the Lyapunov exponent to justify the dynamics of the non-spatial model. A variety of patterns like interference, spot, and stripe are observed with special emphasis on Beddington-DeAngelis function response. These complex patterns explore the beauty of the spatio-temporal model and it can be easily related to real-world biological systems.
物种相互作用的生态理论主要基于竞争、干扰和捕食者 - 猎物模型。在本文中，我们提出并研究了一个三物种捕食者 - 猎物模型，以考察捕食者之间的相互干扰。我们分析了非空间模型的有界性和科尔莫戈罗夫条件。通过稳定性和霍普夫分岔分析来研究系统的动力学行为。估计了时空系统的图灵不稳定性准则。在数值模拟中，带有时间演化图的相图显示了周期性和混沌振荡。分岔图展示了非空间模型非常丰富和复杂的动力学行为。我们计算李雅普诺夫指数以验证非空间模型的动力学。观察到了各种模式，如干扰、斑点和条纹，特别强调了贝丁顿 - 德安吉利斯函数响应。这些复杂模式展现了时空模型之美，并且很容易与现实世界的生物系统联系起来。
