Publication

Cluster synchronization in three-dimensional lattices of diffusively coupled oscillators

Martin Hasler, Igor Belykh
2003
Journal Articles

Abstract

Cluster synchronization modes of continuous time oscillators that are diffusively coupled in a three-dimensional (3-D) lattice are studied in the paper via the corresponding linear invariant manifolds. Depending in an essential way on the number of oscillators composing the lattice in three volume directions, the set of possible regimes of spatiotemporal synchronization is examined. Sufficient conditions of the stability of cluster synchronization are obtained analytically for a wide class of coupled dynamical systems with complicated individual behavior. Dependence of the necessary coupling strengths for the onset of global synchronization on the number of oscillators in each lattice direction is discussed and an approximative formula is proposed. The appearance and order of stabilization of the cluster synchronization modes with increasing coupling between the oscillators are revealed for 2-D and 3-D lattices of coupled Lur'e systems and of coupled Rossler oscillators.

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https://infoscience.epfl.ch/entities/publication/39c4382d-d480-4e36-914d-bed474c215f1

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Martin Hasler, Igor Belykh
2003
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/39c4382d-d480-4e36-914d-bed474c215f1

About this result

Related concepts (32)

Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection.

Bravais lattice

In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by where the ni are any integers, and ai are primitive translation vectors, or primitive vectors, which lie in different directions (not necessarily mutually perpendicular) and span the lattice. The choice of primitive vectors for a given Bravais lattice is not unique.

Complete lattice

In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). A lattice which satisfies at least one of these properties is known as a conditionally complete lattice. Specifically, every non-empty finite lattice is complete. Complete lattices appear in many applications in mathematics and computer science. Being a special instance of lattices, they are studied both in order theory and universal algebra.

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Cluster synchronization in three-dimensional lattices of diffusively coupled oscillators

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