Dynamics Analysis Of Inertial Neural Networks And A Tick Population Model With Multiple Delays

With the constant progress of society and technology the application of functional differential equations in biological mathematics,physics,economics and network sy stems has been developed.They are often used to describe many phenomena and laws in the real world,especially in the study of neural network dynamics and population ecology and other practical problems.Therefore,it is necessary to further study the theory of functional differential equations and their application in various fields.In this master dissertation,the Ly apunov functional approach,differential inequality techniques and fluctuation lemma are applied to study the dynamic properties for a class of neutral-type inertial neural networks incorporating multiple delay s and a tick population model incorporating distinctive time-varying developmental and diapause-induced delays,the main contents include the attractivity of the equilibrium point,the existence and exponential stability of the periodic solution.The dissertation consists of the below four chapters:In Chapter 1,the historical background,research status and significance of the research issues in this article are briefly introduced,then the main content of this study is stated.In Chapter 2,the periodic oscillation properties of solutions for a class of neutraltype inertial neural networks incorporating multiple delay s is explored.By utilizing an approach based on the Lyapunov functional approach coupled with differential inequality techniques.we establish several sufficient assertions to guarantee the existence and exponential convergence on the periodic solutions for the proposed networks,and the computer simulation of a.numerical example is furnished to illustrate the effectiveness of the theoretical results.In addition,the obtained results broaden the application range of neutral-types inertial neural networks.In Chapter 3,the global attractivity of a tick population model incorporating distinctive time-varying developmental and diapause-induced delay s is studied.By exploiting some differential inequality techniques and with the aid of the fluctuation lemma,we first prove the positive,bounded and persistent properties for all solutions of the addressed equation.Consequently,a,delay-dependent,criterion is derived to assure the global attractivity of the positive equilibrium point.Since the obt ained conclusion does not require that delays are constant,which are novel.And lastly,a computer simulation indicates that,the theoretical analysis is consistent with the numerical observation results.In Chapter 4,we give a summary of the research work and prospect to the future research work.