Persistence Analysis And Optimal Control Of A Class Of Stochastic Competitive Population

In nature,the competitive relationship is very common.The different populations will compete for food,resources,living space,etc.With the growth of population,competition within the population also occurs.As a result of competition,it easy to image that the more competitive population survives,and the less competitive population is eliminated by nature.It is in line with the principle of ecological competitive exclusion.But the phenomenon of competition coexisting in nature is common.We want to explore the intricate relationships among competitive populations and obtain stable and persistent conditions for competitive populations to survive.At the same time,it can be obtained the optimal harvesting strategy under the premise of persistent survival of the population.1.Considering a class of stochastic differential algebraic system of competitive populations.We add the prey population of two competing populations to the system,making the system be a three-group system.Especially,we also consider the algebraic equations with economic significance to form a stochastic differential algebra system.First,the existence and uniqueness of the solution of the system is given.Then we give the sufficient conditions for the system to survive.Finally,the persistence of the system is verified by numerical simulation.2.Considering a class of stochastic differential system of competitive populations with Markov switching.First,the sufficient conditions of stochastic persistence and persistence in mean are given.From the proof,we find that the persistence of the system is not only related to the persistence of each state,but also the stationary probability distribution value of each state.Then,under the condition of persistence,the optimal capture strategy is given.Finally,numerical simulations are presented.3.Considering a class of stochastic differential system of competitive populations with time-delay and Markov switching.The system is the three-group model of two competitors and one prey.First,the existence and uniqueness of the solution of the system is given.And the sufficient conditions for persistence in mean are given by the form of lemma.Then,under these conditions,optimal harvesting strategy of three groups is given.Finally,numerical simulations are given for the images of the three groups with random persistence and persistence in mean.