项目名称: 确定混沌与随机混沌系统复杂性研究
项目编号: No.11271139
项目类型: 面上项目
立项/批准年度: 2013
项目学科: 数理科学和化学
项目作者: 杨启贵
作者单位: 华南理工大学
项目金额: 68万元
中文摘要: 在确定性系统解中出现的混沌称为确定混沌,它与随机混沌普遍存在于许多自然过程,研究它们具有重要的科学意义和应用前景。对于n维自治系统,n=2无确定混沌,而出现确定混沌至少n=3,因此对3维确定混沌系统与3维随机混沌系统的定性研究具有特别重要的地位。本项目以3维混沌系统作为研究平台,首先建立3维统一的Lorenz-like型系统和扰动Homilton系统等典型确定混沌系统的全局吸引与稳定性、有界性与正Lyapunov指数、同宿轨或异宿轨、奇异退化异宿环、分支与混沌吸引子等定性结构判据;然后讨论随机扰动对3维确定混沌系统的影响,辅以理论推导和计算机符号推理克服确定混沌或随机混沌系统探讨中的缺点和障碍,研究一般3维确定混沌系统以及在随机扰动下的确定混沌系统诱变的随机混沌、随机分支等定性结构及其相互联系与通往确定混沌或随机混沌的途径,获得一些高维系统的确定混沌与随机混沌复杂性构成机理,并有新的突破。
中文关键词: 确定混沌系统;随机混沌系统;分支与混沌;随机分支与随机混沌;复杂性
英文摘要: The chaotic behavior in deterministic systems is called deterministic chaos. Deterministic chaos and stochastic chaos has been discovered in numerous natural phenomena. The study on them has important scientific significance and potential applications. It is well known that for an n-dimension autonomous system, there exists no chaos for n=2, chaos for at least n=3. Therefore, a qualitatively study of 3-dimension deterministic and stochastic chaotic systems is of particular importance in the study of chaotic systems. The project first establishes some criteria of characteristics, such as global attractivity and stability, boundedness, positive Lyapunov exponents, homoclinic and heteroclinic orbits, singularly degenerate heteroclinic cycles, bifurcation and chaotic attractor for 3-dimension unified Lorenz-type systems, perturbed Hamiltonian systems and other deterministically chaotic systems. Then we study the impact of stochastic perturbation to 3-dimensional deterministic chaotic system. By rigorous mathematical analysis and symbolic computation to get around the difficulty in the study of deterministic chaos and stochastic chaos, we investigate the qualitative structures and their interaction of general 3-dimensional deterministically chaotic system, such as the stochastic chaos and bifurcation induced by the s
英文关键词: deterministic chaotic system;stochastic chaotic system;bifurcation and chaos;stochastic bifurcation and stochastic chaos;complexity