Dynamics of Perturbed Wavetrain Solutions to the Ginzburg‐Landau Equation | Zendy

Keefe Laurence R. | Zendy

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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.

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