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TRANSFORMATION OF LOCAL BIFURCATIONS UNDER COLLOCATION METHODS
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 Title & Authors
TRANSFORMATION OF LOCAL BIFURCATIONS UNDER COLLOCATION METHODS
Foster, Andrew; Khumalo, Melusi;
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 Abstract
Numerical schemes are routinely used to predict the behavior of continuous dynamical systems. All such schemes transform flows into maps, which can possess dynamical behavior deviating from their continuous counterparts. Here the common bifurcations of scalar dynamical systems are transformed under a class of algorithms known as linearized one-point collocation methods. Through the use of normal forms, we prove that each such bifurcation in an originating flow gives rise to an exactly corresponding one in its discretization. The conditions for spurious period doubling behavior under this class of algorithm are derived. We discuss the global behavioral consequences of a singular set induced by the discretizing methods, including loss of monotonicity of solutions, intermittency, and distortion of attractor basins.
 Keywords
collocation methods;spurious behavior;bifurcation;
 Language
English
 Cited by
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Various Closeness Results in Discretized Bifurcations, Differential Equations and Dynamical Systems, 2012, 20, 3, 235  crossref(new windwow)
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Discretizing the transcritical and pitchfork bifurcations – conjugacy results, Journal of Difference Equations and Applications, 2015, 21, 3, 155  crossref(new windwow)
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