TY - JOUR
T1 - Spatiotemporal chaos in spatially extended systems
AU - Cai, David
AU - McLaughlin, David W.
AU - Shatah, Jalal
N1 - Funding Information:
David Cai is supported in part by the Joseph and Hebert Keller Instructorship at New York University, New York and in part by a Sloan Foundation Grant no.96-3-1. David McLaughlin is supported in part by a Sloan Foundation Grant no.96-3-1, AFOSR-49620-98, and NSF DMS-9971813. Jalal Shatah is supported by NSF DMS-9803121.
PY - 2001
Y1 - 2001
N2 - To address finite-size effects in the use of the decay mutual information to characterize spatiotemporal chaotic dynamics, we modify the dispersion of the nonlinear Schrödinger equation to obtain a model system for which the number of unstable modes remains fixed while the domain size increases. Our numerical study of the model system clearly establishes that spatiotemporal chaos arises in the presence of only two unstable modes. In this spatially extended system, the spatiotemporal chaos is characterized by chaotic dynamics in time and by an exponential decay in space of mutual information, with the decay rate becoming system-size independent in the large system-size limit.
AB - To address finite-size effects in the use of the decay mutual information to characterize spatiotemporal chaotic dynamics, we modify the dispersion of the nonlinear Schrödinger equation to obtain a model system for which the number of unstable modes remains fixed while the domain size increases. Our numerical study of the model system clearly establishes that spatiotemporal chaos arises in the presence of only two unstable modes. In this spatially extended system, the spatiotemporal chaos is characterized by chaotic dynamics in time and by an exponential decay in space of mutual information, with the decay rate becoming system-size independent in the large system-size limit.
KW - Non-linear Schrödinger equation
KW - Partial differential equations (PDE)
KW - Spatiotemporal chaos
UR - http://www.scopus.com/inward/record.url?scp=0034920509&partnerID=8YFLogxK
U2 - 10.1016/S0378-4754(00)00299-8
DO - 10.1016/S0378-4754(00)00299-8
M3 - Article
AN - SCOPUS:0034920509
SN - 0378-4754
VL - 55
SP - 329
EP - 340
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
IS - 4-6
ER -