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Chaotic motion of propagating pulses in the Gray-Scott model
Masaaki Yadome1, Kei-Ichi Ueda, Masaharu Nagayama
1Research Institute for Electronic Science, Hokkaido University, Sapporo 060-0812, Japan.
Abstract:
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.
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