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Spatial uniformity in diffusively-coupled systems using weighted L2 norm contractions | IEEE Conference Publication | IEEE Xplore

Spatial uniformity in diffusively-coupled systems using weighted L2 norm contractions


Abstract:

We present conditions that guarantee spatial uniformity in diffusively-coupled systems. Diffusive coupling is a ubiquitous form of local interaction, arising in diverse a...Show More

Abstract:

We present conditions that guarantee spatial uniformity in diffusively-coupled systems. Diffusive coupling is a ubiquitous form of local interaction, arising in diverse areas including multiagent coordination and pattern formation in biochemical networks. The conditions we derive make use of the Jacobian matrix and Neumann eigenvalues of elliptic operators, and generalize and unify existing theory about asymptotic convergence of trajectories of reaction-diffusion partial differential equations as well as compartmental ordinary differential equations. We present numerical tests making use of linear matrix inequalities that may be used to certify these conditions. We discuss an example pertaining to electromechanical oscillators. The paper's main contributions are unified verifiable relaxed conditions that guarantee synchrony.
Date of Conference: 17-19 June 2013
Date Added to IEEE Xplore: 15 August 2013
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Conference Location: Washington, DC, USA

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