Modeling for Spatio-Temporal Chaos

时空混沌建模

• 批准号: 11837014
• 负责人: SAKAGUCHI Hidetsugu
• 金额: $ 1.86万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11837014/
• 关键词: nonlinear equation; spatio-temporal chaos; Burgers equation

To understand spatio-temporal chaos better, we have studied simple model eqations. The creation and annihilation processes of characteristics spatial structures is typical of the spatio-temporal chaos. The reconnection of roll structures is a fundamental process in defect chaos.We have studied the Burgers equation with an additional instability term. A characteristic spatial structure in this system is the shock structure. In the spatio-temporal chaos, there appear many shocks and they collide with each other. Two shocks are merged into one shock as a resut of the collision. A new shock is spontaneously created in a long interval between two neighboring shocks. These creation and merging processes are characteristic of the spatio-temporal chaos in this model equation. We have constructed a simple model for the positions of the shocks and obtained a similar chaotic time evolution including the creation and merging of shocks.We have studied a coupled Ginzburg-Landau equation for another example and found a pulse solution as an attractor. The pulse solution can exhibit breathing motion and splitting bifurcation.As a result, spatio-temporal chaos appears spontaneously from a single pulse solution.

为了更好地理解时空混乱，我们研究了简单的模型架。特征空间结构的创建和歼灭过程是时空混乱的典型特征。滚动结构的重新连接是缺陷混乱中的一个基本过程。我们以额外的不稳定性术语研究了汉堡方程。该系统中的特征空间结构是冲击结构。在时空混乱中，出现了许多冲击，它们相互碰撞。将两次冲击融合为一次冲击，以重新碰撞。在两个相邻的冲击之间以很长的间隔自发产生新的冲击。这些创建和合并过程是该模型方程中时空混乱的特征。我们已经为冲击的位置构建了一个简单的模型，并获得了类似的混乱时间演变，包括创建和合并冲击。我们研究了一个耦合的金茨堡 - Landau方程，以供另一个示例，并找到了脉冲解决方案作为吸引子。脉冲溶液可以表现出呼吸运动和分裂分叉。结果，时空混乱从单个脉冲溶液中自发出现。

项目成果

H.Sakaguchi: "A Simple Model for Spatio-Temporal Chaos in an Unstable Burgers Equation"Progress of Theoretical Physics. 103・4. 703-711 (2000)

H. Sakaguchi：“不稳定伯格斯方程中的时空混沌的简单模型”理论物理进展 103・4（2000）。

H.Sakaguchi: "A SImple Model for Spatio-Temporal Chaos in an Unstable Burgers Equation"Progress of Theoretical Physics. 103. 703-711 (2000)

H.Sakaguchi：“不稳定伯格斯方程中时空混沌的简单模型”理论物理进展。

H,Sakaguchi: "Shock structures in time-averaged patterns for the Kuramoto-Sivashinsky equation"Physical Review E. 62・6. 8817-8819 (2000)

H，Sakaguchi：“Kuramoto-Sivashinsky 方程的时间平均模式中的冲击结构”物理评论 E. 8817-8819 (2000)。

H.Sakaguchi: "Shock structures in time-averaged patterns for the Kuramoto-Sivashinsky equation"Physical Review E. 62. 8817-8819 (2000)

H.Sakaguchi：“Kuramoto-Sivashinsky 方程的时间平均模式中的冲击结构”物理评论 E. 62. 8817-8819 (2000)

"Breathing ans randomly walking pulses in a semilinear Ginzburg-Landau system"Physica D. 147. 273-283 (2000)

“半线性 Ginzburg-Landau 系统中的呼吸和随机行走脉冲”Physica D. 147. 273-283 (2000)