Yadome Masaaki, Ueda Kei-Ichi, Nagayama Masaharu
Research Institute for Electronic Science, Hokkaido University, Sapporo 060-0812, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056207. doi: 10.1103/PhysRevE.83.056207. Epub 2011 May 9.
Transition routes of propagating pulses in the Gray-Scott model from oscillatory to chaotic motion are investigated by numerical studies. Global bifurcation of the Gray-Scott model gives us information about the onset mechanism of transient dynamics, such as the splitting and extinction of pulses. However, the instability mechanism of oscillatory pulses has not been clarified, even numerically. Global bifurcation analysis of time periodic oscillatory traveling pulses, called traveling breathers, enables us to find chaotic motions of oscillatory pulse solutions. Two types of transitions to chaos, namely, period-doubling sequences and breakdown of quasiperiodic solutions, are found near the bifurcation points of traveling breathers.
通过数值研究，探讨了格雷-斯科特模型中传播脉冲从振荡运动到混沌运动的转变路径。格雷-斯科特模型的全局分岔为我们提供了关于瞬态动力学起始机制的信息，例如脉冲的分裂和消失。然而，即使在数值上，振荡脉冲的不稳定性机制也尚未阐明。对时间周期振荡行波脉冲（称为行波呼吸子）进行全局分岔分析，使我们能够找到振荡脉冲解的混沌运动。在行波呼吸子的分岔点附近，发现了两种通向混沌的转变类型，即倍周期序列和准周期解的崩溃。
