本项目旨在研究时标上的（泛函）动力方程的若干理论及应用问题，并主要研究： 1、 完善时标上的概周期动力方程理论,研究时标上的抽象方程的解、概周期解、几乎自守解的存在性及稳定性等； 2、 时标上的分数阶动力方程的周期解、概周期解的存在性及边值问题解的存在性等。 3、 利用不动点定理、拓扑度理论、变分方法和临界点理论研究带有各种边值条件的时标上的（泛函）动力方程解的存在性、多重性，特别是同宿解、异宿解的存在性、多重性问题。 4、 揭示时标上的脉冲（泛函）动力方程的定性性态是如何随时标的粗细度、脉冲、偏差变元改变的。 5、 应用本项目新发展起来的理论研究时标上的生态模型、神经网络模型和经济模型的各种定性性态。 本相目的研究将不仅发展时标动力方程的理论，还将进一步扩展非线先分析的理论和方法及时标动力方程自身的应用范围。具有重要的理论及应用价值。

This project aims to study various qualitative behaviors of functional dynamic equations on time scales and mainly 1. to perfect the theory of almost periodic dynamic equations on time scales; and use these theories to study the existence and stability of solutions, almost periodic solutions,almost automorphic solutions to abstract dynamic equations on time scales; 2. to study the existence of periodic solutions, almost periodic solutions of fractional dynamic equations on time scales and solutions for boundary value problems to these equations; 3. by using fixed point theorems, topological degree theory, variational methods and critical point theory to study the existence and multiplicity of solutions for functional dynamic equations on time scales with various boundary value conditions,especially, to study the existence and multiplicity of homoclinic solutions and heteroclinic solutions; 4.to explore how do the qualitative behaviors of dynamic equations on time scales change with the the graininess of time scales. 5.apply the newly developed theory and methods to study various qualitative behaviers of ecological models, neural network models and economic models on time scales. The research of this project will not only develop the theory of dynamic equations, but also will further extend the own range of applications of nonlinear analysis theory and methods. Hence this project has important theoretical and practical values.