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沌，我们研究了简单的模型方程。特征空间结构的产生和湮灭过程是典型的时空混沌。轧辊结构的重新连接是缺陷混沌中的一个基本过程。我们已经研究了带有附加不稳定性项的Burgers方程。该系统的一个特征空间结构是冲击结构。在时空混沌中，会出现许多冲击，并相互碰撞。由于碰撞，两个激波合并为一个激波。在两个相邻激波之间的较长间隔内会自发地产生一个新的激波。这些产生和合并过程是该模型方程的时空混沌特征。我们建立了一个简单的激波位置模型，得到了一个类似的混沌时间演化，包括激波的产生和合并。对于另一个例子，我们研究了一个耦合的金兹堡-朗道方程，并找到了一个脉冲解作为吸引子。脉冲溶液可以表现出呼吸运动和分裂分叉。结果，时空混沌从单个脉冲解中自发出现。

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: "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: "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 and B.A.Malomed: "Breathing and randomly walking pulses in a semilinear Ginzburg-Landau system"Physica D. 147. 273-282 (2000)

H.Sakaguchi 和 B.A.Malomed：“半线性 Ginzburg-Landau 系统中的呼吸和随机行走脉冲”Physica D. 147. 273-282 (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)