U.S.-Mexico Collaborative Research: Dynamics of Extended Systems and Coupled Map Lattices

美国-墨西哥合作研究：扩展系统动力学和耦合地图格子

• 批准号: 0104675
• 负责人: Mark Levi
• 金额: $ 7.1万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-01 至 2006-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0104675&HistoricalAwards=false
• 关键词: U.S.; Mexico; Collaborative; Research; Dynamics

0104675LeviThis U.S. Mexico award will support Drs. Mark Levi, Howard Weiss, and Yakov Pesin in a research collaboration with Valentine Afraimovich of the Mathematics Department of the Unversidad Autonoma de San Luis de Potosi. The investigators plan to study: 1) Coupled map lattices corresponding to partial differential equations from physics and biology, in particular, the FitzHugh-Nagumo equation (which is of great interest in neurobiology). The collaborators intend to describe the ergodic properties of its local map and construct SRB measures for the attractor of this map. 2) The transition from coupled map lattices to partial differential equations via traveling waves, which will build a foundation for numerical modeling of some partial differential equations of evolution type. 3) The Dynamics of chains of coupled oscillators, in particular, those associated with the Sine-Gordon equation.A coupled map lattice is a discrete time dynamical system whose phase space is of a particular form, and for which the overall system exhibits translational symmetry.Coupled map lattices have recently gained wide popularity as models of spatio-temporal chaos and coherent structures. There is currently great interest in using coupled map lattices to model turbulence, nerve cells, phase transitions in statistical physics, and crystals. They also arise naturally from the discrete version of evolution partial differential equations.

0104675列维这个美国墨西哥奖将支持马克·列维、霍华德、韦斯和雅科夫·佩辛博士与圣路易斯-波托西自治大学数学系的瓦伦丁·伊莫维奇进行研究合作。 研究人员计划研究：1）耦合映射格子对应于物理学和生物学的偏微分方程，特别是FitzHugh-Nagumo方程（在神经生物学中非常感兴趣）。 作者试图描述其局部映射的遍历性质，并构造其吸引子的SRB测度。2)利用行波方法实现了耦合映象格子到偏微分方程的过渡，为某些发展型偏微分方程的数值建模奠定了基础。3)耦合振子链的动力学，特别是与Sine-Gordon方程有关的动力学。耦合映象格子是一种离散时间动力学系统，其相空间具有特定的形式，并且整个系统具有平移对称性。耦合映象格子作为时空混沌和相干结构的模型近年来得到了广泛的应用。目前有很大的兴趣在使用耦合映射格子模型湍流，神经细胞，统计物理学中的相变，和晶体。它们也自然地产生于演化偏微分方程的离散形式。