Bifurcation analysis of a discrete Phytoplankton-Zooplankton model with linear predational response function and toxic substance distribution  

作　　者：A.Q.Khan F.Nazir M.B.Almatrafi 

机构地区：[1]Departmentof Mathematics University of Azad Jammu and Kashmir Muzaffarabad 13100,Pakistan [2]Department of Mathematics College of Science,Taibah University Al-Madinah Al-Munawarah,Saudi Arabia

出　　处：《International Journal of Biomathematics》2023年第4期81-101,共21页生物数学学报（英文版）

基　　金：The research of A.Q.Khan and F.Nazir is partially supported by the Higher Education Commission of Pakistan.

摘　　要：Phytoplanktons are drifting plants in an aquatic system.They provide food for marine animals and are compared to terrestrial plants in that having chlorophyll and carrying out photosynthesis.Zooplanktons are drifting animals found inside the aquatic bodies.For stable aquatic ecosystem,the growth of both Zooplankton and Phytoplankton should be in steady state but in previous eras,there has been a universal explosion in destructive Plankton or algal blooms.Many investigators used various mathematical methodologies to try to explain the bloom phenomenon.So,in this paper,a discretized two-dimensional Phytoplankton-Zooplankton model is investigated.The results for the existence and uniqueness,and conditions for local stability with topological classifications of the equilibrium solutions are determined.It is also exhibited that at trivial and semitrivial equilibrium solutions,discrete model does not undergo fip bifurcation,but it undergoes Neimark-Sacker bifurcation at interior equilibrium solution under certain conditions.Further,state feedback method is deployed to control the chaos in the under consideration system.The extensive numerical simulations are provided to demonstrate theoretical results.

关 键 词：Discrete model numerical simulation BIFURCATIONS CHAOS 

分 类 号：O17[理学—数学]