Lyapunov exponents of the Kuramoto--Sivashinsky PDE

Russell A. Edson, Judith E. Bunder, Trent W. Mattner, Anthony J. Roberts

Abstract


The Kuramoto–Sivashinsky equation is a prototypical chaotic nonlinear partial differential equation (PDE) in which the size of the spatial domain plays the role of a bifurcation parameter. We investigate the changing dynamics of the Kuramoto–Sivashinsky PDE by calculating the Lyapunov spectra over a large range of domain sizes. Our comprehensive computation and analysis of the Lyapunov exponents and the associated Kaplan–Yorke dimension provides new insights into the chaotic dynamics of the Kuramoto–Sivashinsky PDE, and the transition to its one-dimensional turbulence.


doi:10.1017/S1446181119000105

Keywords


Lyapunov exponents, dynamical systems.



DOI: https://doi.org/10.21914/anziamj.v61i0.13939



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.