SOLITON TURBULENCE AND STRANGE ATTRACTOR

Abstract

This study finds that there exists a set of three basic evolution patterns including a dissipative soliton in the non-Hamiltonian media governed by the Ginzburg-Landau equation. A global analysis in the introduced subspace shows that the soliton is a spiral sink enclosed by a doubly connected homoclinic orbit. The soliton, prior to a turbulent state, breaks up into recurring pulses through a Hopf bifurcation. The strange attractor underlying the turbulence is found and presented with discussion. The Lyapunov number, found from a one-dimensional reduction of the attractor, is given by L almost-equal-to 0.34.