Tuesday, February 02, 2016

"Heterogeneous, Weakly Coupled Map Lattices"

A new paper of mine just came out in final form today (though the typesetters were supposed to send us another set of page proofs, and sure enough issues that we pointed out with references leading to dead links in the references still have not been fixed completely). In any event, while we attempt to get them to correct their mistakes, here are some details about the article.

Title: Heterogeneous, Weakly Coupled Map Lattices

Authors: Ma Dolores Sotelo Herrera, Jesús San Martín, and Mason A. Porter

Abstract: Coupled map lattices (CMLs) are often used to study emergent phenomena in nature. It is typically assumed (unrealistically) that each component is described by the same map, and it is important to relax this assumption. In this paper, we characterize periodic orbits and the laminar regime of type-I intermittency in heterogeneous weakly coupled map lattices (HWCMLs). We show that the period of a cycle in an HWCML is preserved for arbitrarily small coupling strengths even when an associated uncoupled oscillator would experience a period-doubling cascade. Our results characterize periodic orbits both near and far from saddle–node bifurcations, and we thereby provide a key step for examining the bifurcation structure of heterogeneous CMLs.

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