Name
Title | ||
|---|---|---|
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 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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/ACC.2013.6580717 | American Control Conference |
Keywords | DocType | ISSN |
Jacobian matrices,eigenvalues and eigenfunctions,linear matrix inequalities,mathematical operators,oscillators,partial differential equations,reaction-diffusion systems,synchronisation,Jacobian matrix,Neumann eigenvalues,compartmental ordinary differential equations,diffusively-coupled systems,electromechanical oscillators,elliptic operators,linear matrix inequalities,local interaction ubiquitous form,numerical tests,reaction-diffusion partial differential equations,spatial uniformity,synchrony,trajectory asymptotic convergence,unified verifiable relaxed conditions,weighted L2 norm contractions | Conference | 0743-1619 |
ISBN | Citations | PageRank |
978-1-4799-0177-7 | 1 | 0.37 |
References | Authors | |
6 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| S. Yusef Shafi | 1 | 45 | 4.94 |
| Zahra Aminzare | 2 | 17 | 3.58 |
| murat arcak | 3 | 1855 | 195.31 |
| Eduardo D. Sontag | 4 | 3134 | 781.88 |