Department of Applied Mathematics, Indian Institute of Technology (ISM) Dhanbad, Dhanbad 826004, India.
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China.
Math Biosci Eng. 2019 May 23;16(5):4660-4691. doi: 10.3934/mbe.2019234.
This work is mainly focused on the series of dynamical analysis of tritrophic food chain model with Sokol-Howell functional response, incorporating the multiple gestation time delays for more realistic formulation. Basic properties of the proposed model are studied with the help of boundedness, stability analysis, and Hopf-bifurcation theory. By choosing the fixed parameter set and varying the value of time delay, the stability of the model has been studied. There is a critical value for delay parameter. Steady state is stable when the value of delay is less than the critical value and further increase the value of delay beyond the critical value makes the system oscillatory through Hopf-bifurcation. Whereas, another delay parameter has a stabilizing effect on the system dynamics. Chaotic dynamics has been explored in the model with the help of phase portrait and sensitivity on initial condition test. Numerical simulations are performed to validate the effectiveness of the derived theoretical results and to explore the various dynamical structures such as Hopf-bifurcation, periodic solutions and chaotic dynamics.
这项工作主要集中在具有 Sokol-Howell 功能反应的三营养食物链模型的一系列动力学分析上，纳入了多个妊娠时间延迟以进行更现实的表述。借助有界性、稳定性分析和 Hopf 分支理论研究了所提出模型的基本性质。通过选择固定参数集并改变时滞值，可以研究模型的稳定性。存在一个延迟参数的临界值。当延迟值小于临界值时，稳态是稳定的，进一步增加延迟值超过临界值会通过 Hopf 分支使系统产生振荡。而另一个延迟参数对系统动力学具有稳定作用。借助相图和初始条件测试的敏感性，在模型中探索了混沌动力学。进行数值模拟以验证所推导的理论结果的有效性，并探索各种动力学结构，如 Hopf 分支、周期解和混沌动力学。
