dorsal/arxiv
View Schema2D pattern evolution constrained by complex network dynamics
| Authors | Luis Enrique Correa da Rocha, Luciano da Fontoura Costa |
|---|---|
| Categories | |
| ArXiv ID | physics/0610001 |
| URL | https://arxiv.org/abs/physics/0610001 |
| DOI | 10.1088/1367-2630/9/4/108 |
| Journal | New J. Phys. 9, 108 (2007) |
Abstract
Complex networks have established themselves along the last years as being particularly suitable and flexible for representing and modeling several complex natural and human-made systems. At the same time in which the structural intricacies of such networks are being revealed and understood, efforts have also been directed at investigating how such connectivity properties define and constrain the dynamics of systems unfolding on such structures. However, lesser attention has been focused on hybrid systems, \textit{i.e.} involving more than one type of network and/or dynamics. Because several real systems present such an organization (\textit{e.g.} the dynamics of a disease coexisting with the dynamics of the immune system), it becomes important to address such hybrid systems. The current paper investigates a specific system involving a diffusive (linear and non-linear) dynamics taking place in a regular network while interacting with a complex network of defensive agents following Erd\"os-R\'enyi and Barab\'asi-Albert graph models, whose nodes can be displaced spatially. More specifically, the complex network is expected to control, and if possible to extinguish, the diffusion of some given unwanted process (\textit{e.g.} fire, oil spilling, pest dissemination, and virus or bacteria reproduction during an infection). Two types of pattern evolution are considered: Fick and Gray-Scott. The nodes of the defensive network then interact with the diffusing patterns and communicate between themselves in order to control the spreading. The main findings include the identification of higher efficiency for the Barab\'asi-Albert control networks.
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"abstract": "Complex networks have established themselves along the last years as being\nparticularly suitable and flexible for representing and modeling several\ncomplex natural and human-made systems. At the same time in which the\nstructural intricacies of such networks are being revealed and understood,\nefforts have also been directed at investigating how such connectivity\nproperties define and constrain the dynamics of systems unfolding on such\nstructures. However, lesser attention has been focused on hybrid systems,\n\\textit{i.e.} involving more than one type of network and/or dynamics. Because\nseveral real systems present such an organization (\\textit{e.g.} the dynamics\nof a disease coexisting with the dynamics of the immune system), it becomes\nimportant to address such hybrid systems. The current paper investigates a\nspecific system involving a diffusive (linear and non-linear) dynamics taking\nplace in a regular network while interacting with a complex network of\ndefensive agents following Erd\\\"os-R\\\u0027enyi and Barab\\\u0027asi-Albert graph models,\nwhose nodes can be displaced spatially. More specifically, the complex network\nis expected to control, and if possible to extinguish, the diffusion of some\ngiven unwanted process (\\textit{e.g.} fire, oil spilling, pest dissemination,\nand virus or bacteria reproduction during an infection). Two types of pattern\nevolution are considered: Fick and Gray-Scott. The nodes of the defensive\nnetwork then interact with the diffusing patterns and communicate between\nthemselves in order to control the spreading. The main findings include the\nidentification of higher efficiency for the Barab\\\u0027asi-Albert control networks.",
"arxiv_id": "physics/0610001",
"authors": [
"Luis Enrique Correa da Rocha",
"Luciano da Fontoura Costa"
],
"categories": [
"physics.comp-ph",
"cond-mat.dis-nn",
"physics.soc-ph"
],
"doi": "10.1088/1367-2630/9/4/108",
"journal_ref": "New J. Phys. 9, 108 (2007)",
"title": "2D pattern evolution constrained by complex network dynamics",
"url": "https://arxiv.org/abs/physics/0610001"
},
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