Study On The Stability Of A Diabetes Model

This article mainly introduces an alternative method to calculate ordinary differential equations(ODEs)and the Lyapunov exponents of the dynamic system they describe.For a given ordinary differential equation and its related variational equation,approximations of two piecewise linear ODEs are made.The Lyapunov exponent is then calculated based on the solutions to these two piecewise linear ordinary differential equations.This method is closely related to the local linearization method(LL method)of the ordinary differential equations.The main advantage is that these piecewise linear ordinary differential equations may be fully integrated in a non-simultaneous manner.This article uses numerical examples to illustrate the performance of the method.When applied to real life,for example,when detecting a certain chaotic behavior,many nonlinear systems will appear.The regulation of blood sugar balance studied in this paper is one of the important conditions for maintaining the steady state of human body's internal environment,and also a key component of the regulation of human's life activity.The unbalance of human body's blood sugar regulation will cause a variety of diseases,and one of them with a high incidence in daily life is diabetes.Diabetes cannot be completely cured by existing medical methods.For early treatment,measures like strict diet,medication,or regular insulin injections are effective.However,it may cause systemic complications or even threaten human's life in some severe cases.To understand more about diabetes,we need to understand the process of blood sugar control in humans.Thus,in-depth study of the process of blood sugar regulation plays an important role in diabetes prevention and treatment.It is a very intuitive way to judge the chaos of a dynamic system by calculating its Lyapunov exponents.Among them,only the first few Lyapunov exponents(usually only the largest one)are important.This article will analyze the chaotic characteristics of a kinetic system by calculating its numerical solution,periodic solution and Lyapunov exponent,and apply the research results to the detection and treatment of diabetes.