How Synchronization Protects from Noise
Publication Date
January 15, 2010
Journal
PLOS Computational Biology
Authors
Nicolas Tabareau, Jean Jacques Slotine & Quang Cuong Pham
Volume
6
Issue
1
Pages
e1000637
DOI
https://dx.plos.org/10.1371/journal.pcbi.1000637
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1000637
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/20090826
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2797083
Europe PMC
http://europepmc.org/abstract/MED/20090826
Web of Science
000274231500009
Scopus
76749128055
Mendeley
http://www.mendeley.com/research/synchronization-protects-noise
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Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/867246"], "description"=>"<p>The dynamics of coupled FN oscillators are given by equation (2). The parameters used in all simulations are , , . (A) shows the trajectory of the “membrane potential” of a noise-free oscillator and (B) depicts the frequency spectrum of this trajectory computed by Fast Fourier Transformation. (C) and (D) present the trajectory (respectively the frequency spectrum) of a <i>noisy uncoupled</i> oscillator (). (E) and (F) show the trajectory (respectively the frequency spectrum) of a <i>noisy synchronized</i> oscillator within an all-to-all network (, , ). Note the temporal and frequential similarities between a noise-free oscillator and a noisy synchronized one. For instance, the main frequency and the first harmonics are very similar in the two frequency spectra. In contrast, the frequency spectrum of a noisy uncoupled oscillator shows no clear harmonics.</p>", "links"=>[], "tags"=>["fn", "oscillators", "euler-maruyama", "algorithm"], "article_id"=>537701, "categories"=>["Neuroscience", "Information And Computing Sciences"], "users"=>["Nicolas Tabareau", "Jean-Jacques Slotine", "Quang-Cuong Pham"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000637.g001", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulations_of_a_network_of_FN_oscillators_using_the_Euler_Maruyama_algorithm_47_/537701", "title"=>"Simulations of a network of FN oscillators using the Euler-Maruyama algorithm [47].", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 03:03:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/867526"], "description"=>"<p>(A) shows the trajectory of the “membrane potential” of an oscillator in the network. (B) shows its frequency spectrum. Compare these two plots with those in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000637#pcbi-1000637-g001\" target=\"_blank\">Figure 1</a>.</p>", "links"=>[], "tags"=>["probabilistic", "symmetric"], "article_id"=>537990, "categories"=>["Neuroscience", "Information And Computing Sciences"], "users"=>["Nicolas Tabareau", "Jean-Jacques Slotine", "Quang-Cuong Pham"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000637.g004", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulation_for_a_probabilistic_symmetric_network__/537990", "title"=>"Simulation for a probabilistic symmetric network (, , , ).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 03:04:44"}
  • {"files"=>["https://ndownloader.figshare.com/files/867621"], "description"=>"<p>(A) The time-varying input voltage. (B) Trajectory of the “membrane potential” of a noise-free oscillator. (C) Trajectory of a <i>noisy uncoupled</i> oscillator. (D) Trajectory of a <i>noisy synchronized</i> oscillator (, , ).</p>", "links"=>[], "tags"=>["hindmarsh-rose", "oscillators", "varying"], "article_id"=>538084, "categories"=>["Neuroscience", "Information And Computing Sciences"], "users"=>["Nicolas Tabareau", "Jean-Jacques Slotine", "Quang-Cuong Pham"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000637.g005", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulation_of_Hindmarsh_Rose_oscillators_with_time_varying_inputs_/538084", "title"=>"Simulation of Hindmarsh-Rose oscillators with time varying inputs.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 03:05:14"}
  • {"files"=>["https://ndownloader.figshare.com/files/867389"], "description"=>"<p>Note that the same set of random initial conditions was used in the two plots. (A) shows the average “membrane potential” computed over <i>noisy uncoupled</i> oscillators (). (B) shows the average “membrane potential” computed over <i>noisy synchronized</i> oscillators within an all-to-all network (, ). Observe that, in the first plot, the average trajectory of uncoupled oscillators carries essentially no information, while in the second plot, the average trajectory of synchronized oscillators is very similar to a noise-free one.</p>", "links"=>[], "tags"=>["fn"], "article_id"=>537857, "categories"=>["Neuroscience", "Information And Computing Sciences"], "users"=>["Nicolas Tabareau", "Jean-Jacques Slotine", "Quang-Cuong Pham"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000637.g002", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_8220_Spatial_mean_8221_of_FN_oscillators_/537857", "title"=>"“Spatial mean” of FN oscillators.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 03:03:59"}
  • {"files"=>["https://ndownloader.figshare.com/files/867459"], "description"=>"<p>Note that the experimental expectations were computed assuming the ergodic hypothesis. (A) Expectation of the average squared distance between the 's and (given by ) as a function of the coupling strength (). Theoretical bound (cf equations (7) and (4)) for (bold line), for (plain line), for (dashed line); simulation results for (squares), for (triangles), for (crosses). (B) Expected squared distance between a noisy synchronized oscillator and its observer (given by ) as a function of (, ). The bound was plotted in plain line and the simulation results were represented by crosses.</p>", "links"=>[], "tags"=>["appraisal"], "article_id"=>537929, "categories"=>["Neuroscience", "Information And Computing Sciences"], "users"=>["Nicolas Tabareau", "Jean-Jacques Slotine", "Quang-Cuong Pham"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000637.g003", "stats"=>{"downloads"=>2, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Asymptotic_appraisal_of_the_theoretical_bounds_/537929", "title"=>"Asymptotic appraisal of the theoretical bounds.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 03:04:23"}

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Relative Metric

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