Mathematical Simulation Study On Jellyfish Control

With complex life history and body structure,jellyfish is an important species in marine ecosystem.In recent years,jellyfish outbreaks have become more and more frequent,causing great harm to the ecological environment.The complex life history of jellyfish can be simulated by appropriate mathematical models.Therefore,in order to study the change of jellyfish population,it is necessary to establish a mathematical model to control the jellyfish population.In this thesis,taking the amount of jellyfish and natural enemies as the indexes of jellyfish control,establish Filippov and state dependent pulse jellyfish control model to simulate the control process of jellyfish.The first chapter introduces the preparatory knowledge needed for this thesis.In chapter two,the interaction between polyp and jellyfish is considered,and the amount of jellyfish population is taken as the index of jellyfish control.It is assumed that jellyfish population is density-dependent and polyp population is non-density-dependent.When the amount of jellyfish population is less than the economic threshold,no control is applied;otherwise,when the amount of jellyfish is larger than the economic threshold,natural enemies of the ephyra are released to the sea area where jellyfish live,which reduces the survival rate of the ephyra,and then reduces the reproduction rate of polyp to jellyfish.Then a polypjellyfish Filippov jellyfish control model is established.The dynamics of the subsystem and Filippov system are systematically analyzed,and the existence of boundary focus branch and boundary node branch are discussed.The existence conditions and globally asymptotic stability conditions of real,virtual,pseudo and boundary equilibria are obtained.The existence regions of corresponding equilibria under different parameter values are given.The results show that jellyfish can be controlled by adjusting the release rate of natural enemies,thus reducing the survival rate of the ephyra.In chapter three and chapter four,the interaction between jellyfish and natural enemies is considered.It is assumed that the growth rate of jellyfish from sexual reproduction of polyps is constant.Considering that if the natural enemies population reaches a critical index,the jellyfish population can be kept within the desired range,so the amount of natural enemies is taken as the index of jellyfish control.When the amount of natural enemies is more than the critical index,no control is applied;otherwise,the natural enemies is released.At this point,there are two different control strategies,namely continuous control and instantaneous control.In chapter three,considering the continuous release of natural enemies,the Filippov jellyfish control model is established,and the dynamics of the model are comprehensively analyzed,and the conditions for controlling jellyfish population within the desired range are given.In chapter 4,considering the instantaneous release of natural enemies,the state-dependent impulsive jellyfish control model is established.The existence and globally asymptotic stability of order-1 periodic solution and the nonexistence of order-2 periodic solution are discussed.The results show that the amount of jellyfish population can be controlled in a stable periodic solution by increasing the releasing rate of natural enemies,and the amount of jellyfish population and natural enemies population oscillates periodically.