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DYNAMICS IN TIME-DELAY RECURRENTLY COUPLED OSCILLATORS
2011
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
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A model of time-delay recurrently coupled spatially segregated neural oscillators is proposed. ...
Bifurcation analysis shows the richness of the dynamical behaviors in a biophysically plausible parameter region. ...
Dynamics in Time-Delay Recurrently Coupled Oscillators 779 0 1 2 3 4 5 6 −8 −6 −4 −2 0 2 4 6 8 η=γ+1/γ η=γ−1/γ η=−γ+1/γ η=−γ−1/γ γ η D 1 D 1 D 3 D 2 Fig. 1. ...
doi:10.1142/s0218127411028787
fatcat:vnwhqux7ajhmhef37wztgmke7q
Neuronal Multistability Induced by Delay
[chapter]
2007
Lecture Notes in Computer Science
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In this contribution we study how a delayed circuit representing a recurrent synaptic connection interferes with neuronal nonlinear dynamics. ...
The neuron is modeled using a Hodgkin-Huxley type model in which the firing pattern depends on subthreshold oscillations, and the feedback is included as a time delayed linear term in the membrane voltage ...
the delay time of the mutual coupling. ...
doi:10.1007/978-3-540-74690-4_98
fatcat:irogcuodgbex3gx7pzn3kvscoa
Visualization of coupling in time series by order recurrence plots
2005
Physical Review E
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We introduce a method to visualize dependencies between two time series by applying the concept of cross recurrence plots to the local ordinal structure. ...
Connections to the instantaneous phase and the determination of phase coupling of two coupled Rössler systems in the standard and funnel regimes are shown. ...
First we define the symbolic dynamics and introduce order recurrence plots. On coupled oscillators we demonstrate the ability to visualize and quantify the coupling strength. ...
doi:10.1103/physreve.72.046220
pmid:16383525
fatcat:n3xwz2kownbqhj4p4fkxgprdby
Recurrent events of synchrony in complex networks of pulse-coupled oscillators
2011
Europhysics letters
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2014 pre-print arXiv:1403.0101v1 fatcat:32zvekvgevcnhlpelbpunnis4m
We present and analyze deterministic complex networks of pulse-coupled oscillators that exhibits recurrent events comprised of an increase and a decline in synchrony. ...
The phenomenon is specific to spatial networks with both short- and long-ranged connections and requires delayed interactions and refractoriness of oscillators. ...
The phenomenon relies on both refractoriness in the local dynamics and delayed excitatory coupling and is specific to networks with both short-and long-ranged connections. ...
doi:10.1209/0295-5075/95/38001
fatcat:comhx2kq25e6bitcvx66gdxygu
Phase synchronization in unidirectionally coupled Ikeda time-delay systems
2008
The European Physical Journal Special Topics
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Phase synchronization in unidirectionally coupled Ikeda time-delay systems exhibiting non-phase-coherent hyperchaotic attractors of complex topology with highly interwoven trajectories is studied. ...
The existence of phase synchronization is also further confirmed by typical transitions in the Lyapunov exponents of the coupled Ikeda time-delay systems and also using the concept of localized sets. ...
III we discuss briefly about the Ikdea time-delay systems and its dynamics. ...
doi:10.1140/epjst/e2008-00832-6
fatcat:lyfimonuqjalhlr7avyvtarbhi
Global phase synchronization in an array of time-delay systems
2010
Physical Review E
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2010 pre-print arXiv:1007.2804v1 fatcat:6a2y3fgxmjhsjehmfpaowbafpq
In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. ...
We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors ...
time-delay systems and analyse the mechanism behind the dynamical organization of the coupled oscillators to form GPS. ...
doi:10.1103/physreve.82.016215
pmid:20866715
fatcat:zxrmenyssfapxodvq25ksg64ue
Earthquake sequencing: Chimera states with Kuramoto model dynamics on directed graphs
2015
Nonlinear Processes in Geophysics Discussions
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Since mapping of global stress-field fluctuations in real time at all scales is an impossible task, we consider an earthquake zone as a proxy for a collection of weakly-coupled oscillators, the dynamics ...
We propose that they are akin to the dynamics of the collective behaviour of weakly-coupled non-linear oscillators. ...
We would like to express deep gratitude to the Department of Mathematics and Statistics for support and computing time and to the generosity and hospitality shown at the Max Planck Institute for the Physics ...
doi:10.5194/npgd-2-361-2015
fatcat:vh5ilwmrbbb3ndyyk32lpoblle
Phase synchronization in time-delay systems
2006
Physical Review E
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We have found these transitions in coupled piece-wise linear and in Mackey-Glass time-delay systems. ...
Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase coherent hyperchaotic ...
synchronization phenomena in the coupled time-delay systems ͑1͒ by means of very recently proposed methods based on recurrence plots ͓26͔. ...
doi:10.1103/physreve.74.035205
pmid:17025694
fatcat:kp4kkyiuk5da5onxztronur3du
Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs
2015
Nonlinear Processes in Geophysics
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Since mapping of global stress-field fluctuations in real time at all scales is an impossible task, we consider an earthquake zone as a proxy for a collection of weakly coupled oscillators, the dynamics ...
We propose that they are akin to the dynamics of the collective behavior of weakly coupled non-linear oscillators. ...
We would like to express deep gratitude to the Department of Mathematics and Statistics for support and computing time and to the generosity and hospitality shown at the Max Planck Institute for the Physics ...
doi:10.5194/npg-22-499-2015
fatcat:jg6xpvozqveijgzwx7s5g4exzi
Influence of time-delayed feedback in the firing pattern of thermally sensitive neurons
2004
Physical Review E
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We analyze the dynamics of the neuron depending on the temperature, the synaptic strength, and the delay time. ...
The model is modified to include a feedback loop that is represented by two parameters: the synaptic strength and the transmission delay time. ...
In particular, our goal is to investigate the effect of a recurrent loop in the dynamics of subthreshold oscillations that operate close to but below that the spiking threshold. ...
doi:10.1103/physreve.70.031904
pmid:15524546
fatcat:fyp4tm3it5cljbsvl3srrq4kxy
Dendritic and Axonal Propagation Delays Determine Emergent Structures of Neuronal Networks with Plastic Synapses
2017
Scientific Reports
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In a minimal setting, characterized by neglecting dendritic and axonal propagation delays, STDP eliminates bidirectional connections between two coupled neurons and turns them into unidirectional connections ...
We here take into account how propagation delays, composed of dendritic and axonal delay times, may affect the temporal order of spikes. ...
a neuronal oscillator the synaptic efficacies can be taken as constants and the theory of delayed coupled oscillators can be applied to determine the phase lag of firing of the neurons in the stable phase-locked ...
doi:10.1038/srep39682
pmid:28045109
pmcid:PMC5206725
fatcat:vvdt7jo4freftfkqyuxvoxpl5e
Transition from phase to generalized synchronization in time-delay systems
2008
Chaos
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The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without ...
We report the identification of phase synchronization in coupled nonidentical piece-wise linear and in coupled Mackey-Glass time-delay systems with highly non-phase-coherent regimes. ...
CPS from recurrence quantification analysis The complex synchronization phenomena in the coupled time-delay systems ͑4͒ can also be analyzed by means of the very recently proposed methods based on recurrence ...
doi:10.1063/1.2911541
pmid:18601485
fatcat:7tdps6odtve47pzlevvmebydba
Quantitative prediction of intermittent high-frequency oscillations in neural networks with supralinear dendritic interactions
2010
Proceedings of the National Academy of Sciences of the United States of America
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Accordingly, the differences in conduction delays are neglected, so synchronous presynaptic spiking can be amplified. ...
This article considers the implications of supralinear dendritic interactions as mediated by fast dendritic spikes in larger recurrent neural networks. ...
In model IN, the frequency of oscillations depends on strengths and delays of recurrent connectivity, external stimulation, and single-cell properties. ...
doi:10.1073/pnas.0909615107
pmid:20511534
pmcid:PMC2890715
fatcat:msrz3nlmebb3vey5kmzgs6ipru
GLOBAL AND PARTIAL PHASE SYNCHRONIZATIONS IN ARRAYS OF PIECEWISE LINEAR TIME-DELAY SYSTEMS
2012
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
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In this paper, we report the identification of global and partial phase synchronizations in linear arrays of unidirectionally coupled piecewise linear time-delay systems with two different coupling configurations ...
We confirm the occurrence of both global and partial phase synchronizations in two different piecewise linear time-delay systems using various numerical methods. ...
This study can also be extended to twodimensional lattices of coupled time-delay systems with and without delay coupling and in networks of time-delay systems with indirect global dynamic environment coupling ...
doi:10.1142/s0218127412501787
fatcat:rkz4qu4m7bbg3izmvmv2l4nooa
Limits to detection of generalized synchronization in delay-coupled chaotic oscillators
2013
Physical Review E
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To that end, we analyze synchronization in a generalized sense of delay-coupled chaotic oscillators in unidirectional ring configurations. ...
This has major consequences for the interpretation of the dynamics of coupled systems and applications thereof. ...
The oscillators in the ring are delay coupled, with a total delay in the loop of τ d . We focus on elements X, Y, and Z. ...
doi:10.1103/physreve.88.062924
pmid:24483548
fatcat:upkv4xrqgzgedhmqb2aa7emwpi
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