混沌是非线性科学的一个重要研究方向。三维自治动力系统中的混沌已被广泛研究了，并找到了它在工程等领域的实际应用。然而，高维自治系统或随机系统中混沌是如何产生的，以及它如何应用于电子工程、保密通信等领域，是一个全新的研究方向。本项目基于动力学定性理论方法将主要研究：(1) 如何构造具有任意给定多个平衡点的混沌系统，又如何分析其动力学行为，目的是理解高维混沌系统的基本动力学特征与性质；（2）高维自治系统中奇异退化同宿轨和奇异退化异宿环分别是如何导致混沌的，目的是揭示此类动力系统中混沌产生的本质机制；（3）无穷维系统中分布混沌是如何产生的，目的揭示分布意义下混沌的产生机制；（4）随机系统（包括分数阶的Brown运动和Levy过程驱动的混沌系统）的分支和混沌是如何产生的，目的是揭示随机混沌与随机分叉之间的内在关联。本项目的研究不仅可以丰富混沌动力学的内容，而且可以进一步为混沌的实际应用奠定理论基础。

Chaos is an important research direction of nonlinear sciences. Chaos in 3-dimensional autonomous dynamical systems has been intensively and extensively studied and has been found to have practical applications in the engineering field. However, how chaos is generated in high-dimensional autonomous system and stochastic system as well as how it is applied to fields such as electric engineering and communication security is a novel research direction. Based on methods of qualitative theory in dynamics, this project will focus on studying: (1) how a chaotic system with arbitrarily any number of equilibrium points is constructed, and how its dynamical behavior is analyzed, with the aim to understand fundamental dynamical characteristics and properties; (2) how degenerate heteroclinic or homoclinic orbits result in chaos in high-dimensional systems, with the aim to reveal the essential mechanism of generating chaos in these systems; (3) how distributed chaos is generated in infinite systems, with the aim to reveal how chaos is generated in a distribution sense; (4) how bifurcation and chaos in random systems (including those with fractional-order Brown motion or driven by Levy processes) are generated, with the aim to uncover the essential correlation between stochastic bifurcation and chaos. These studies may not only enrich the content of chaos dynamics but also lay a theoretical foundation for chaos applications.