Pal Pinaki, Kumar Krishna, Maity Priyanka, Dana Syamal Kumar
Department of Mathematics, National Institute of Technology, Durgapur-713 209, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Feb;87(2):023001. doi: 10.1103/PhysRevE.87.023001. Epub 2013 Feb 4.
We report the pattern dynamics in the vicinity of an inverse homoclinic bifurcation in an extended dissipative system. We observe, in direct numerical simulations of three dimensional Rayleigh-Bénard convection with stress-free top and bottom plates, a spontaneous breaking of a competition of two mutually perpendicular sets of oscillating cross rolls to one of two possible sets of oscillating cross rolls as the Rayleigh number is raised above a critical value. The time period of the oscillating cross-roll patterns diverges and shows scaling behavior near the bifurcation point. This is an example of a transition from nonlocal to local pattern dynamics near an inverse homoclinic bifurcation. We also present a simple four-mode model that captures the pattern dynamics quite well.
我们报道了一个扩展耗散系统中逆同宿分岔附近的模式动力学。在对顶部和底部板无应力的三维瑞利 - 贝纳德对流的直接数值模拟中，我们观察到，当瑞利数升高到临界值以上时，两组相互垂直的振荡交叉滚之间的竞争会自发地打破，形成两组可能的振荡交叉滚中的一组。振荡交叉滚模式的时间周期发散，并在分岔点附近呈现标度行为。这是一个在逆同宿分岔附近从非局部模式动力学向局部模式动力学转变的例子。我们还提出了一个简单的四模模型，它能很好地捕捉模式动力学。
