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Chaos in high-dimensional dissipative dynamical systems
Ispolatov Iaroslav, , Allende Sebastian, Doebeli Michael
Published in Springer Science and Business Media LLC
Volume: 5
Issue: 1

For dissipative dynamical systems described by a system of ordinary differential equations, we address the question of how the probability of chaotic dynamics increases with the dimensionality of the phase space. We find that for a system of d globally coupled ODE’s with quadratic and cubic non-linearities with randomly chosen coefficients and initial conditions, the probability of a trajectory to be chaotic increases universally from ~10−5 − 10−4 for d = 3 to essentially one for d ~ 50. In the limit of large d, the invariant measure of the dynamical systems exhibits universal scaling that depends on the degree of non-linearity, but not on the choice of coefficients and the largest Lyapunov exponent converges to a universal scaling limit. Using statistical arguments, we provide analytical explanations for the observed scaling, universality and for the probability of chaos.

About the journal
JournalData powered by TypesetScientific Reports
PublisherData powered by TypesetSpringer Science and Business Media LLC
Open AccessNo