A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Michel F. Randrianandrasana; Xueyong Wei; David Lowe

doi:10.1016/j.cnsns.2010.09.011

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Michel F. Randrianandrasana, Xueyong Wei, David Lowe

College of Engineering and Physical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

Original language	English
Pages (from-to)	2945-2956
Number of pages	12
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	16
Issue number	7
DOIs	https://doi.org/10.1016/j.cnsns.2010.09.011
Publication status	Published - Jul 2011

Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in Communications in nonlinear science and numerical simulation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Randrianandrasana, Michel F.; Wei, Xueyong and Lowe, David. A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators. Communications in nonlinear science and numerical simulation, 16, 7, (2011). DOI: 10.1016/j.cnsns.2010.09.011

Keywords

duffing resonator
van der Pol oscillator
MEMS
emergent collective behaviour

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10.1016/j.cnsns.2010.09.011

CNSNS_paper.pdf
NOTICE: this is the author’s version of a work that was accepted for publication in Communications in nonlinear science and numerical simulation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Randrianandrasana, Michel F.; Wei, Xueyong and Lowe, David. A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators. Communications in nonlinear science and numerical simulation, 16, 7, (2011). DOI: 10.1016/j.cnsns.2010.09.011

http://dx.doi.org/10.1016/j.cnsns.2010.09.011

Cite this

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title = "A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators",

abstract = "Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.",

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A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Abstract

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Keywords

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