Establishment And Analysis Of Two Classes Of High-Dimensional Differential Models

In this paper,the corresponding high-dimensional differential models for two specific biological background problems are established and analyzed,one type of model is studied from the molecular level,and the other type of model is studied from the population level,the specific work is as follows:Aiming at the possible molecular mechanism of the non-desensitization of receptor AT1R by the autoantibody(AT1-AA)of the angiotensin-II-1 type receptors,a corresponding high-dimensional differential system was established and the figures were modeled.First,the dynamic system of high-dimension differential equations of the control group(normal pregnant women)and experimental group(AT1R non-desensitization possible molecules mechanism:endocytosis disorders and conformation changes)were established.Then,graphs fitting and analysis of each model using least square method,compare the size of AIC,values in each model,and obtain the possible key molecular mechanism of AT1R non-desensitization is endocytosis disorders.A four-dimensional predator-prey model with two delays was established aiming at the hunting time and maturity period of two influencing factors among populations and qualitative analysis was performed.First,the conditions for the stable positive equilibrium for the four-dimensional predator-prey model were given.Taking the predator time and the maturation period of the delay term as parameters,the sufficient conditions for the existence of the Hopf bifurcation at the positive equilibrium are given.At the same time,when T1+ T2 = T0,the system generates the Hopf branch;finally,the appropriate parameter value is taken.Numerical simulation was performed to verify the consistency between theoretical results and numerical calculations.