Premium
Dynamics of Perturbed Wavetrain Solutions to the Ginzburg‐Landau Equation
Author(s) -
Keefe Laurence R.
Publication year - 1985
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198573291
Subject(s) - attractor , chaotic , lyapunov exponent , mathematics , bifurcation , limit (mathematics) , instability , mathematical analysis , dynamics (music) , torus , physics , statistical physics , classical mechanics , mathematical physics , nonlinear system , quantum mechanics , geometry , artificial intelligence , computer science , acoustics
The bifurcation structure and asymptotic dynamics of even, spatially periodic solutions to the time‐dependent Ginzburg‐Landau equation are investigated analytically and numerically. All solutions spring from unstable periodic modulations of a uniform wavetrain. Asymptotic states include limit cycles, two‐tori, and chaotic attractors. Lyapunov exponents for some chaotic motions are obtained. These show the solution strange attractors to have a fractal dimension slightly greater than 3.