Timme, Marc

[["dc.bibliographiccitation.artnumber","065201"],["dc.bibliographiccitation.issue","6"],["dc.bibliographiccitation.journal","PHYSICAL REVIEW E"],["dc.bibliographiccitation.volume","78"],["dc.contributor.author","Kirst, Christoph"],["dc.contributor.author","Timme, Marc"],["dc.date.accessioned","2018-11-07T11:08:50Z"],["dc.date.available","2018-11-07T11:08:50Z"],["dc.date.issued","2008"],["dc.description.abstract","We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each other's basin volume. This counterintuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed interactions. We analytically show that upon continuously removing a local noninvertibility of the system, the two unstable attractors become a set of two nonattracting saddle states that are heteroclinically connected. This transition equally occurs from larger networks of unstable attractors to heteroclinic structures and constitutes a new type of singular bifurcation in dynamical systems."],["dc.description.sponsorship","Federal Ministry of Education & Research (BMBF) [01GQ0430]"],["dc.identifier.doi","10.1103/PhysRevE.78.065201"],["dc.identifier.isi","000262240600003"],["dc.identifier.pmid","19256893"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/52878"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Physical Soc"],["dc.relation.issn","2470-0053"],["dc.relation.issn","2470-0045"],["dc.title","From networks of unstable attractors to heteroclinic switching"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1606"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","IEEE Transactions on Automatic Control"],["dc.bibliographiccitation.lastpage","1619"],["dc.bibliographiccitation.volume","62"],["dc.contributor.author","Klinglmayr, Johannes"],["dc.contributor.author","Bettstetter, Christian"],["dc.contributor.author","Timme, Marc"],["dc.contributor.author","Kirst, Christoph"],["dc.date.accessioned","2020-12-10T18:26:15Z"],["dc.date.available","2020-12-10T18:26:15Z"],["dc.date.issued","2017"],["dc.description.abstract","The theory of pulse-coupled oscillators provides a framework to formulate and develop self-organizing synchronization strategies for wireless communications and mobile computing. These strategies show low complexity and are adaptive to changes in the network. Even though several protocols have been proposed and theoretical insight was gained there is no proof that guarantees synchronization of the oscillator phases in general dynamic coupling topologies under technological constraints. Here, we introduce a family of coupling strategies for pulse-coupled oscillators and prove that synchronizationemerges for systems with arbitrary connected and dynamic topologies, individually changing signal propagation and processing delays, and stochastic pulse emission. It is shown by simulations how unreliable links or intentionally incomplete communication between oscillators can improve synchronization performance."],["dc.identifier.doi","10.1109/TAC.2016.2593642"],["dc.identifier.eissn","1558-2523"],["dc.identifier.isi","000399033000005"],["dc.identifier.issn","0018-9286"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/76014"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","PUB_WoS_Import"],["dc.publisher","Ieee-inst Electrical Electronics Engineers Inc"],["dc.relation.issn","1558-2523"],["dc.relation.issn","0018-9286"],["dc.title","Convergence of Self-Organizing Pulse-Coupled Oscillator Synchronization in Dynamic Networks"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","2119"],["dc.bibliographiccitation.issue","7"],["dc.bibliographiccitation.journal","SIAM Journal on Applied Mathematics"],["dc.bibliographiccitation.lastpage","2149"],["dc.bibliographiccitation.volume","70"],["dc.contributor.author","Kirst, Christoph"],["dc.contributor.author","Timme, Marc"],["dc.date.accessioned","2018-11-07T08:48:35Z"],["dc.date.available","2018-11-07T08:48:35Z"],["dc.date.issued","2010"],["dc.description.abstract","Pulse-coupled threshold units serve as paradigmatic models for a wide range of complex systems. When the state variable of a unit crosses a threshold, the unit sends a pulse that is received by other units, thereby mediating the interactions. At the same time, the state variable of the sending unit is reset. Here we present and analyze a class of pulse-coupled oscillators where the reset may be partial only and is mediated by a partial reset function. Such a partial reset characterizes intrinsic physical or biophysical features of a unit, e. g., resistive coupling between dendrite and soma of compartmental neurons; at the same time the description in terms of a partial reset enables a rigorous mathematical investigation of the collective network dynamics. The partial reset acts as a desynchronization mechanism. For N all-to-all pulse-coupled oscillators an increase in the strength of the partial reset causes a sequence of desynchronizing bifurcations from the fully synchronous state via states with large clusters of synchronized units through states with smaller clusters to complete asynchrony. By considering inter-and intracluster stability we derive sufficient and necessary conditions for the existence and stability of cluster states on the partial reset function and on the intrinsic dynamics of the oscillators. For a specific class of oscillators we obtain a rigorous derivation of all N-1 bifurcation points and demonstrate that already arbitrarily small changes in the reset function may produce the entire sequence of bifurcations. We illustrate that the transition is robust against structural perturbations and prevails in the presence of heterogeneous network connectivity and changes in the intrinsic oscillator dynamics."],["dc.identifier.doi","10.1137/09074749X"],["dc.identifier.isi","000281108800002"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/21248"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Siam Publications"],["dc.relation.issn","0036-1399"],["dc.title","PARTIAL RESET IN PULSE-COUPLED OSCILLATORS"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]