TY - JOUR
T1 - Invading wave fronts and their oscillatory wakes are linked by a modulated travelling phase resetting wave
AU - Sherratt, Jonathan A.
PY - 1998
Y1 - 1998
N2 - Periodic wave trains are the generic solution form for oscillatory reaction-diffusion equations in one space dimension. It has been shown previously that invasive wavefronts generate behind them a wave train with a different speed from that of the invasion [Sherratt, Physica D 70 (1994) 370-382]. In this paper, the mechanism of wave train generation is studied in detail for systems of two reaction-diffusion equations close to a supercritical Hopf bifurcation in the kinetics, with equal diffusion coefficients. A combination of analytical and numerical evidence is presented suggesting that the invasive front and wave train are separated by a modulated travelling wave of phase gradient, in which phase singularities occur periodically. This calculation leads to a prediction of the amplitude and speed of the wave train generated by invasion. Copyright © 1998 Elsevier Science B.V.
AB - Periodic wave trains are the generic solution form for oscillatory reaction-diffusion equations in one space dimension. It has been shown previously that invasive wavefronts generate behind them a wave train with a different speed from that of the invasion [Sherratt, Physica D 70 (1994) 370-382]. In this paper, the mechanism of wave train generation is studied in detail for systems of two reaction-diffusion equations close to a supercritical Hopf bifurcation in the kinetics, with equal diffusion coefficients. A combination of analytical and numerical evidence is presented suggesting that the invasive front and wave train are separated by a modulated travelling wave of phase gradient, in which phase singularities occur periodically. This calculation leads to a prediction of the amplitude and speed of the wave train generated by invasion. Copyright © 1998 Elsevier Science B.V.
KW - Oscillatory systems
KW - Reaction-diffusion
KW - Travelling waves
KW - Wave trains
UR - http://www.scopus.com/inward/record.url?scp=0001218738&partnerID=8YFLogxK
U2 - 10.1016/S0167-2789(97)00317-5
DO - 10.1016/S0167-2789(97)00317-5
M3 - Article
VL - 117
SP - 145
EP - 166
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 1-4
ER -