Study On Existence Of Traveling Wave Solutions For A Class Of Infectious Disease Model And Time Delay Feedback Control For A Class Of Axial Moving SMA Laminated Beam System

In this paper,we have studied two practical problems with different backgrounds.First,we studied the existence of travelling wave solutions in a three-dimension-al infectious disease model composed of SIR and SIS.The stabilities,under certain conditions,of disease-free equilibrium point and endemic disease equilibrium point in this model are discussed by means of Routh-Hurwitz criterion.Moreover,using Schauder fixed point theorem,the existence of travelling wave solutions connecting those two equilibrium points is investigated via constructing appropriate upper-lower solutions.The proof result shows that wnen R0>1,for any c>c*,there exists travelling wave solution with the minimum wave speed c*,which connect the disease-free equilibrium point and endemic equilibrium point in the epidemic model.Secondly,the purpose is to study the main resonance phenomenon with two different time delays in the axial motion SMA laminated beam system.The multi-scale method is used to solve the approximate analytical solution of the nonlinear equation.The objective function and constraint conditions are set as the value range of the attenuation rate and feedback gain coefficient of the control system respectively.Moreover,the steady-state solution and its stability under various resonance conditions are further analyzed.Finally,the optimal time delay of the controller design is obtained.The research results show that both the feedback gain coefficient and the time delay can control the nonlinear characteristics of the system with good control effect.This result is helpful for the popularization and application of time-delay feedback control in axial motion system,and has important practical value for the design of optimal controllers.