TY - JOUR
T1 - Traveling wave into an unstable state in dissipative oscillator chains
AU - Alfaro-Bittner, K.
AU - Clerc, M. G.
AU - ROJAS CORTES, RENE GABRIEL
AU - GARCIA ÑUSTES, MONICA AMPARO
N1 - Publisher Copyright:
© 2019, Springer Nature B.V.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/10/1
Y1 - 2019/10/1
N2 - Coupled oscillators can exhibit complex spatiotemporal dynamics. Here, we study the propagation of nonlinear waves into an unstable state in dissipative coupled oscillators. To this, we consider the dissipative Frenkel–Kontorova model, which accounts for a chain of coupled pendulums or Josephson junctions and coupling superconducting quantum interference devices. As a function of the dissipation parameter, the front that links the stable and unstable state is characterized by having a transition from monotonous to non-monotonous profile. In the conservative limit, these traveling nonlinear waves are unstable as a consequence of the energy released in the propagation. Traveling waves into unstable states are peculiar of dissipative coupling systems. When the coupling and the dissipation parameter are increased, the average front speed decreases. Based on an averaging method, we analytically determine the front speed. Numerical simulations show a quite fair agreement with the theoretical predictions. To show that our results are generic, we analyze a chain of coupled logistic equations. This model presents the predicted dynamics, opening the door to investigate a wider class of systems.
AB - Coupled oscillators can exhibit complex spatiotemporal dynamics. Here, we study the propagation of nonlinear waves into an unstable state in dissipative coupled oscillators. To this, we consider the dissipative Frenkel–Kontorova model, which accounts for a chain of coupled pendulums or Josephson junctions and coupling superconducting quantum interference devices. As a function of the dissipation parameter, the front that links the stable and unstable state is characterized by having a transition from monotonous to non-monotonous profile. In the conservative limit, these traveling nonlinear waves are unstable as a consequence of the energy released in the propagation. Traveling waves into unstable states are peculiar of dissipative coupling systems. When the coupling and the dissipation parameter are increased, the average front speed decreases. Based on an averaging method, we analytically determine the front speed. Numerical simulations show a quite fair agreement with the theoretical predictions. To show that our results are generic, we analyze a chain of coupled logistic equations. This model presents the predicted dynamics, opening the door to investigate a wider class of systems.
KW - coupled oscillators
KW - Front propagation
KW - Nonlinear wave
UR - http://www.scopus.com/inward/record.url?scp=85073696370&partnerID=8YFLogxK
U2 - 10.1007/s11071-019-05270-5
DO - 10.1007/s11071-019-05270-5
M3 - Article
AN - SCOPUS:85073696370
VL - 98
SP - 1391
EP - 1402
JO - Nonlinear Dynamics
JF - Nonlinear Dynamics
SN - 0924-090X
IS - 2
ER -