dorsal/arxiv
View SchemaStable Concurrent Synchronization in Dynamic System Networks
| Authors | Quang-Cuong Pham, Jean-Jacques Slotine |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0510051 |
| URL | https://arxiv.org/abs/q-bio/0510051 |
| DOI | 10.1016/j.neunet.2006.07.008 |
Abstract
In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple ``rhythms'' interacting and functional assemblies combining neural oscillators of many different types. Mathematically, stable concurrent synchronization corresponds to convergence to a flow-invariant linear subspace of the global state space. We derive a general condition for such convergence to occur globally and exponentially. We also show that, under mild conditions, global convergence to a concurrently synchronized regime is preserved under basic system combinations such as negative feedback or hierarchies, so that stable concurrently synchronized aggregates of arbitrary size can be constructed. Robustnesss of stable concurrent synchronization to variations in individual dynamics is also quantified. Simple applications of these results to classical questions in systems neuroscience and robotics are discussed.
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"abstract": "In a network of dynamical systems, concurrent synchronization is a regime\nwhere multiple groups of fully synchronized elements coexist. In the brain,\nconcurrent synchronization may occur at several scales, with multiple\n``rhythms\u0027\u0027 interacting and functional assemblies combining neural oscillators\nof many different types. Mathematically, stable concurrent synchronization\ncorresponds to convergence to a flow-invariant linear subspace of the global\nstate space. We derive a general condition for such convergence to occur\nglobally and exponentially. We also show that, under mild conditions, global\nconvergence to a concurrently synchronized regime is preserved under basic\nsystem combinations such as negative feedback or hierarchies, so that stable\nconcurrently synchronized aggregates of arbitrary size can be constructed.\nRobustnesss of stable concurrent synchronization to variations in individual\ndynamics is also quantified. Simple applications of these results to classical\nquestions in systems neuroscience and robotics are discussed.",
"arxiv_id": "q-bio/0510051",
"authors": [
"Quang-Cuong Pham",
"Jean-Jacques Slotine"
],
"categories": [
"q-bio.NC"
],
"doi": "10.1016/j.neunet.2006.07.008",
"title": "Stable Concurrent Synchronization in Dynamic System Networks",
"url": "https://arxiv.org/abs/q-bio/0510051"
},
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