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Coupling leads to chaos. (English) Zbl 1133.34027
From the abstract: The main goal of this paper is to prove analytically the existence of strange attractors in a family of vector fields consisting of two Brusselators linearly coupled by diffusion. We will show that such a family contains a generic unfolding of a 4-dimensional nilpotent singularity of codimension \(4\). On the other hand, we will prove that in any generic unfolding \(X_\mu\) of an \(n\)-dimensional nilpotent singularity of codimension \(n\) there are bifurcation curves of \((n-1)\)-dimensional nilpotent singularities of codimension \(n-1\) which are in turn generically unfolded by \(X_\mu\). Arguments conclude recalling that any generic unfolding of the \(3\)-dimensional nilpotent singularity of codimension \(3\) exhibits strange attractors.

34C28 Complex behavior and chaotic systems of ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34D45 Attractors of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Matlab; Mathematica
Full Text: DOI
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