Timme, Marc

[["dc.bibliographiccitation.artnumber","015108"],["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Chaos: An Interdisciplinary Journal of Nonlinear Science"],["dc.bibliographiccitation.lastpage","16"],["dc.bibliographiccitation.volume","16"],["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Geisel, Theo"],["dc.contributor.author","Wolf, Fred"],["dc.date.accessioned","2017-09-07T11:46:16Z"],["dc.date.available","2017-09-07T11:46:16Z"],["dc.date.issued","2006"],["dc.description.abstract","We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is determined by multiple operators, for which standard analysis is not suitable. We describe a general nonstandard solution to the multioperator problem. Subsequently, we derive a class of neuronal rise functions for which all stability operators become degenerate and standard eigenvalue analysis becomes a suitable tool. Interestingly, this class is found to consist of networks of leaky integrate-and-fire neurons. For random networks of inhibitory integrate-and-fire neurons, we then develop an analytical approach, based on the theory of random matrices, to precisely determine the eigenvalue distributions of the stability operators. This yields the asymptotic relaxation time for perturbations to the synchronous state which provides the characteristic time scale on which neurons can coordinate their activity in such networks. For networks with finite in-degree, i.e., finite number of presynaptic inputs per neuron, we find a speed limit to coordinating spiking activity. Even with arbitrarily strong interaction strengths neurons cannot synchronize faster than at a certain maximal speed determined by the typical in-degree.The individual units of many physical systems, from the planets of our solar system to the atoms in a solid, typically interact continuously in time and without significant delay. Thus at every instant of time such a unit is influenced by the current state of its interaction partners. Moreover, particles of many-body systems are often considered to have very simple lattice topology (as in a crystal) or no prescribed topology at all (as in an ideal gas). Many important biological systems are drastically different: their units are interacting by sending and receiving pulses at discrete instances of time. Furthermore, biological systems often exhibit significant delays in the couplings and very complicated topologies of their interaction networks. Examples of such systems include neurons, which interact by stereotyped electrical pulses called action potentials or spikes; crickets, which chirp to communicate acoustically; populations of fireflies that interact by short light pulses. The combination of pulse-coupling, delays, and complicated network topology formally makes the dynamical system to be investigated a high dimensional, heterogeneous nonlinear hybrid system with delays. Here we present an exact analysis of aspects of the dynamics of such networks in the case of simple one-dimensional nonlinear interacting units. These systems are simple models for the collective dynamics of recurrent networks of spiking neurons. After briefly presenting stability results for the synchronous state, we show how to use the theory of random matrices to analytically predict the eigenvalue distribution of stability matrices and thus derive the speed of synchronization in terms of dynamical and network parameters. We find that networks of neural oscillators typically exhibit speed limits and cannot synchronize faster than a certain bound defined by the network topology."],["dc.identifier.doi","10.1063/1.2150775"],["dc.identifier.gro","3151890"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/8722"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","1054-1500"],["dc.title","Speed of synchronization in complex networks of neural oscillators: Analytic results based on Random Matrix Theory"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","821"],["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Geisel, Theo"],["dc.contributor.author","Wolf, F."],["dc.date.accessioned","2017-11-21T15:34:02Z"],["dc.date.available","2017-11-21T15:34:02Z"],["dc.date.issued","2001"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/10167"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.relation.eventend","2001-11-15"],["dc.relation.eventlocation","San Diego"],["dc.relation.eventstart","2001-11-10"],["dc.relation.ispartof","Society for Neuroscience Abstracts"],["dc.title","Synchronization and Desynchronization in Neural Networks with General Connectivity"],["dc.type","conference_abstract"],["dc.type.internalPublication","unknown"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","068101"],["dc.bibliographiccitation.issue","6"],["dc.bibliographiccitation.journal","Physical Review Letters"],["dc.bibliographiccitation.volume","102"],["dc.contributor.author","Kirst, Christoph"],["dc.contributor.author","Geisel, Theo"],["dc.contributor.author","Timme, Marc"],["dc.date.accessioned","2018-11-07T08:32:45Z"],["dc.date.available","2018-11-07T08:32:45Z"],["dc.date.issued","2009"],["dc.description.abstract","The response of a neuron to synaptic input strongly depends on whether or not the neuron has just emitted a spike. We propose a neuron model that after spike emission exhibits a partial response to residual input charges and study its collective network dynamics analytically. We uncover a desynchronization mechanism that causes a sequential desynchronization transition: In globally coupled neurons an increase in the strength of the partial response induces a sequence of bifurcations from states with large clusters of synchronously firing neurons, through states with smaller clusters to completely asynchronous spiking. We briefly discuss key consequences of this mechanism for more general networks of biophysical neurons."],["dc.identifier.doi","10.1103/PhysRevLett.102.068101"],["dc.identifier.fs","503776"],["dc.identifier.isi","000263389500068"],["dc.identifier.pmid","19257635"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/7964"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/17412"],["dc.notes.intern","Merged from goescholar"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Physical Soc"],["dc.relation.issn","0031-9007"],["dc.relation.orgunit","Fakultät für Physik"],["dc.rights","CC BY 3.0"],["dc.rights.uri","https://creativecommons.org/licenses/by/3.0"],["dc.title","Sequential Desynchronization in Networks of Spiking Neurons with Partial Reset"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","194"],["dc.bibliographiccitation.journal","European Journal of Neuroscience"],["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Geisel, Theo"],["dc.contributor.author","Wolf, F."],["dc.date.accessioned","2017-11-22T09:24:42Z"],["dc.date.available","2017-11-22T09:24:42Z"],["dc.date.issued","2000"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/10177"],["dc.language.iso","en"],["dc.notes.status","new -primates"],["dc.title","Unstable synchronization in networks of integrate-and-fire neurons"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dspace.entity.type","Publication"]]

[["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Wolf, F."],["dc.contributor.author","Geisel, Theo"],["dc.date.accessioned","2017-11-21T15:25:37Z"],["dc.date.available","2017-11-21T15:25:37Z"],["dc.date.issued","2001"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/10165"],["dc.language.iso","en"],["dc.notes.status","new -primates"],["dc.relation.ispartof","265. WE-Heraeus Seminar “Synchronization in Physics and Neuroscience.”"],["dc.title","Unstable synchronization and switching among unstable attractors in spiking neural networks"],["dc.type","book_chapter"],["dc.type.internalPublication","unknown"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","258701"],["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.issue","25"],["dc.bibliographiccitation.journal","Physical Review Letters"],["dc.bibliographiccitation.lastpage","4"],["dc.bibliographiccitation.volume","89"],["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Wolf, Fred"],["dc.contributor.author","Geisel, Theo"],["dc.date.accessioned","2017-09-07T11:46:15Z"],["dc.date.available","2017-09-07T11:46:15Z"],["dc.date.issued","2002"],["dc.description.abstract","For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is determined by a multitude of linear operators. We treat this multioperator problem exactly and show that for inhibitory interactions the synchronous state is stable, independent of the parameters and the network connectivity. In randomly connected networks with strong interactions this synchronous state, displaying regular dynamics, coexists with a balanced state exhibiting irregular dynamics. External signals may switch the network between qualitatively distinct states."],["dc.identifier.doi","10.1103/physrevlett.89.258701"],["dc.identifier.gro","3151876"],["dc.identifier.pmid","12484926"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/8708"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0031-9007"],["dc.title","Coexistence of Regular and Irregular Dynamics in Complex Networks of Pulse-Coupled Oscillators"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","074103"],["dc.bibliographiccitation.issue","7"],["dc.bibliographiccitation.journal","Physical Review Letters"],["dc.bibliographiccitation.volume","92"],["dc.contributor.author","Denker, Michael"],["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Diesmann, Markus"],["dc.contributor.author","Wolf, Fred"],["dc.contributor.author","Geisel, Theo"],["dc.date.accessioned","2017-09-07T11:46:16Z"],["dc.date.available","2017-09-07T11:46:16Z"],["dc.date.issued","2004"],["dc.description.abstract","For networks of pulse-coupled oscillators with complex connectivity, we demonstrate that in the presence of coupling heterogeneity precisely timed periodic firing patterns replace the state of global synchrony that exists in homogenous networks only. With increasing disorder, these firing patterns persist until a critical temporal extent is reached that is of the order of the interaction delay. For stronger disorder the periodic firing patterns cease to exist and only asynchronous, aperiodic states are observed. We derive self-consistency equations to predict the precise temporal structure of a pattern from a network of given connectivity and heterogeneity. Moreover, we show how to design heterogeneous coupling architectures to create an arbitrary prescribed pattern."],["dc.identifier.doi","10.1103/physrevlett.92.074103"],["dc.identifier.gro","3151874"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/8705"],["dc.language.iso","en"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.relation.issn","0031-9007"],["dc.title","Breaking Synchrony by Heterogeneity in Complex Networks"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","154105"],["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.issue","15"],["dc.bibliographiccitation.journal","Physical Review Letters"],["dc.bibliographiccitation.lastpage","4"],["dc.bibliographiccitation.volume","89"],["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Wolf, Fred"],["dc.contributor.author","Geisel, Theo"],["dc.date.accessioned","2021-11-22T14:31:54Z"],["dc.date.available","2021-11-22T14:31:54Z"],["dc.date.issued","2002"],["dc.description.abstract","We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are unstable. These unstable attractors occur in networks of pulse-coupled oscillators, and become prevalent with increasing network size for a wide range of parameters. They are enclosed by basins of attraction of other attractors but are remote from their own basin volume such that arbitrarily small noise leads to a switching among attractors"],["dc.identifier.doi","10.1103/PhysRevLett.89.154105"],["dc.identifier.gro","3151884"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/7966"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/93413"],["dc.language.iso","en"],["dc.notes.intern","Migrated from goescholar"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","1079-7114"],["dc.relation.issn","0031-9007"],["dc.rights","CC BY 3.0"],["dc.rights.access","openAccess"],["dc.rights.uri","https://creativecommons.org/licenses/by/3.0"],["dc.subject","networks; unstable"],["dc.title","Prevalence of Unstable Attractors in Networks of Pulse-Coupled Oscillators"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","244103"],["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.issue","24"],["dc.bibliographiccitation.journal","Physical Review Letters"],["dc.bibliographiccitation.lastpage","4"],["dc.bibliographiccitation.volume","93"],["dc.contributor.author","Zumdieck, Alexander"],["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Geisel, Theo"],["dc.contributor.author","Wolf, Fred"],["dc.date.accessioned","2017-09-07T11:46:13Z"],["dc.date.available","2017-09-07T11:46:13Z"],["dc.date.issued","2004"],["dc.description.abstract","We show that long chaotic transients dominate the dynamics of randomly diluted networks of pulse-coupled oscillators. This contrasts with the rapid convergence towards limit cycle attractors found in networks of globally coupled units. The lengths of the transients strongly depend on the network connectivity and vary by several orders of magnitude, with maximum transient lengths at intermediate connectivities. The dynamics of the transients exhibit a novel form of robust synchronization. An approximation to the largest Lyapunov exponent characterizing the chaotic nature of the transient dynamics is calculated analytically."],["dc.identifier.doi","10.1103/physrevlett.93.244103"],["dc.identifier.gro","3151866"],["dc.identifier.pmid","15697818"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/8697"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0031-9007"],["dc.title","Long Chaotic Transients in Complex Networks"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","074101"],["dc.bibliographiccitation.issue","7"],["dc.bibliographiccitation.journal","Physical Review Letters"],["dc.bibliographiccitation.volume","92"],["dc.contributor.author","Geisel, Theo"],["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Wolf, Fred"],["dc.date.accessioned","2018-11-07T10:51:07Z"],["dc.date.available","2018-11-07T10:51:07Z"],["dc.date.issued","2004"],["dc.description.abstract","We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in dependence on the dynamical and network parameters. Furthermore, we show that the speed of synchronization is limited by the network connectivity and remains finite, even if the coupling strength becomes infinite. In addition, our results indicate that synchrony is robust under structural perturbations of the network dynamics."],["dc.identifier.doi","10.1103/PhysRevLett.92.074101"],["dc.identifier.gro","3151886"],["dc.identifier.isi","000189139500024"],["dc.identifier.pmid","14995853"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/48815"],["dc.language.iso","en"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","American Physical Soc"],["dc.relation.issn","0031-9007"],["dc.title","Topological speed limits to network synchronization"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]