TRAVELING WAVES AND CHAOS IN THE KOLMOGOROV-SPIEGEL-SIVASHINSKY MODEL


UNAL G., SUHUBI E.

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, vol.30, no.5, pp.593-610, 1992 (SCI-Expanded) identifier identifier

Abstract

Kolmogorov-Spiegel-Sivashinsky (KSS) equation has been derived to model large-scale structures arising in two-dimensional turbulence [Nucl. Phys. (Proc. Suppl.) 2, 453 (1987)]. In the present study, we have obtained its periodic, quasi-periodic and solitary wave solutions analytically to a certain degree of approximation by discarding the linear damping term. Normal form analysis succeeds to capture Hopf, Neimark and infinite-period bifurcations before the onset of chaos. Melnikov analysis has been carried out to identify the homoclinic bifurcation. Transient spatio-temporal chaos has been observed, by constructing the Poincare-section and it has been identified by computing Lyapunov Characteristic Exponents (LCE).