Lyapunov exponents of the Kuramoto--Sivashinsky PDE
Keywords:Lyapunov exponents, dynamical systems.
AbstractThe Kuramotoâ€“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 Kuramotoâ€“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 Kaplanâ€“Yorke dimension provides new insights into the chaotic dynamics of the Kuramotoâ€“Sivashinsky PDE, and the transition to its one-dimensional turbulence. doi:10.1017/S1446181119000105
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