Dynamics Of A Microcystis-Filter Feeding Fish Population Ecological Model With Aggregation Effect

In this paper,we mainly study the dynamics of a population ecological model of microcystis-filter feeding fish with aggregation effect,and deeply discuss some related dynamics problems in the hot spot field,and obtain more perfect and important theoretical and numerical results.The first chapter mainly introduces the research background and current situation of microcystis population aggregation behavior and algae population dynamics model,and provides the basic concepts,previous knowledge and important lemmas commonly used in the paper,which are the premise of the subsequent chapters.In the second chapter,we build a kind of microcystis-filter feeding fish population dynamics model with aggregation effect,and carry out theoretical analysis and numerical simulation research on it.We deduce the critical threshold conditions of transcritical bifurcation,saddle node bifurcation,Hopf bifurcation and Bogdanov-Takens bifurcation of the model,and numerically simulate the evolution process of specific dynamic behavior of the model,so as to clarify the aggregation effect of microcystis.It also affects the dynamic relationship between microcystis and filter feeding fish.The results show that: if the accumulation area of microcystis exceeds a certain threshold,the filter feeding fish population will become extinct,which also shows that only when the accumulation area of microcystis is below a certain threshold,the filter feeding fish algae control technology will play an effective role.In the third chapter,based on the results of the second chapter,when the accumulation area of microcystis exceeds the critical threshold,the measures of fishing microcystis population and releasing filter feeding fish are taken to control the outbreak of microcystis bloom.In order to study the effectiveness of this kind of control measures,the third chapter constructs a group pulse control model of microcystis filter feeding fish species with aggregation effect,deduces the key critical conditions of specific dynamic behavior of the model,and verifies the effectiveness of the theoretical results by numerical simulation,which indicates the feasibility of microcystis bloom control measures.