Convergence On Two Classes Of Functional Differential Equations

In recent years,the theory of functional differential equations is widely used in various fields of natural and social science,especially in epidemic transmission,biological ecology and neural network dynamics.The main methods used in this thesis are the Dini deriva-tive theory,the analysis technique of the differential inequality and the Lyapunov function method.The convergence of the solutions to a class of n-dimensional differential equations with time-varying delays and a class of inertial neural networks with time-varying delays are studied.The full text consists of the following three parts.In Chapter 1,the research background,significance and development of issues in this thesis are introduced.The main research contents of this paper are addressed as well.In Chapter 2,we consider a class of n-dimensional non-autonomous differential equa-tions with time-varying delays.Employing the differential inequality approach and the Dini derivative theory,it is shown that every solution of the addressed equations tends to a constant vector as t?? oo.Not only the Bernfeld-Haddock conjecture is extended to n-dimensional non-autonomous system,but also the results in the previous literature are improved.In addition,we verify the validity of our results by numerical simulation.In chapter 3,a class of non-autonomous inertial neural networks with time-varying delays and coefficients is explored.By combining Lyapunov function method with differ-ential inequality approach,some novel assertions are gained to guarantee the existence and exponential stability of periodic solutions for the addressed model.The obtained results also suggest that every solution of the addressed model and its derivatives are exponentially convergent to the periodic solution and its derivatives,respectively.The non-reduced or-der method adopted in this paper provides a possible way to research the topic on periodic dynamics of other inertial neural networks.Last but not least,our research works and the prospect of our future research are summarized.