Dynamic Analysis Of Two Fractional-Order Intraguild Predation Models

In recent years,biomathematics,as an interdisciplinary subject,has been paid more and more attention,among which the fitting,prediction and regulation of species number in ecosystem have been widely concerned.In order to study the variation law of species quantity in nature,the fractional population dynamics equation established by combining the fractional dynamic system theory and ecological reality has important theoretical and practical application significance in many aspects such as protection,development,utilization and regulation of population resources.In view of the limitation of the order of the integer-order intraguild predation model and the inaccuracy of the constant predation rate,and in combination with the characteristics of memory and heredity of species growth that can be well described by fractional differential equations,a fractional-order intraguild predation model with Holling-? functional response function is proposed;the stability of the model is studied by using the stability theory of fractional differential equations,and the sufficient conditions for the local asymptotic stability of each equilibrium point are given;taking the order of the model as the critical parameter,the critical conditions of Hopf bifurcation at the positive equilibrium point are studied;finally,a series of numerical experiments are carried out to verify the validity of the theoretical results.On the basis of studying the fractional intraguild predation model,a fractional intraguild predation model with time lag effect is proposed to solve the problem that it takes a certain time for the predator to prey on the prey;the stability of the model is analyzed by using the stability theory of fractional delay differential equations,and the sufficient conditions for the local asymptotic stability of each equilibrium point are given;taking the constant time delay of the model as the critical parameter,the conditions of Hopf bifurcation at the positive equilibrium point are studied;finally,through numerical experiments,the time series evolution diagram of each population in the model is drawn,and the validity and accuracy of the theoretical derivation are verified.Bifurcation of the model can be effectively avoided by controlling the order and delay of the model.The research results of two kinds of fractional predation models provide a theoretical basis for the stability and sustainable development of ecological resources.The paper has 4 pictures,and 53 references.