IMPOSSIBILITY OF ASYMPTOTIC SYNCHRONIZATION FOR PULSE-COUPLED OSCILLATORS WITH DELAYED EXCITATORY COUPLING

2009 ◽  
Vol 19 (06) ◽  
pp. 425-435 ◽  
Author(s):  
WEI WU ◽  
TIANPING CHEN
Keyword(s):  
Coupled Oscillators ◽  
East Asian ◽  
Coupled Oscillator ◽  
Dynamic Behaviors ◽  
Transmission Delays ◽  
Oscillator Networks ◽  
Coupled Networks ◽  
Pulse Coupled Oscillators ◽  
Asymptotic Synchronization ◽  
Coupled Oscillator Model

Fireflies, as one of the most spectacular examples of synchronization in nature, have been investigated widely. In 1990, Mirollo and Strogatz proposed a pulse-coupled oscillator model to explain the synchronization of South East Asian fireflies (Pteroptyx malaccae). However, transmission delays were not considered in their model. In fact, when transmission delays are introduced, the dynamic behaviors of pulse-coupled networks change a lot. In this paper, pulse-coupled oscillator networks with delayed excitatory coupling are studied. A concept of synchronization, named weak asymptotic synchronization, which is weaker than asymptotic synchronization, is proposed. We prove that for pulse-coupled oscillator networks with delayed excitatory coupling, weak asymptotic synchronization cannot occur.

scholarly journals Computing with Arrays of Coupled Oscillators: An Application to Preattentive Texture Discrimination

1990 ◽  
Vol 2 (4) ◽  
pp. 458-471 ◽  
Author(s):  
Pierre Baldi ◽  
Ronny Meir
Keyword(s):  
Long Range ◽  
Cortical Neurons ◽  
Coupled Oscillators ◽  
Dynamic Evolution ◽  
Coupled Oscillator ◽  
Texture Discrimination ◽  
Oscillator Networks ◽  
Neural Computations ◽  
Different Populations ◽  
Experimental Findings

Recent experimental findings (Gray et al. 1989; Eckhorn et al. 1988) seem to indicate that rapid oscillations and phase-lockings of different populations of cortical neurons play an important role in neural computations. In particular, global stimulus properties could be reflected in the correlated firing of spatially distant cells. Here we describe how simple coupled oscillator networks can be used to model the data and to investigate whether useful tasks can be performed by oscillator architectures. A specific demonstration is given for the problem of preattentive texture discrimination. Texture images are convolved with different sets of Gabor filters feeding into several corresponding arrays of coupled oscillators. After a brief transient, the dynamic evolution in the arrays leads to a separation of the textures by a phase labeling mechanism. The importance of noise and of long range connections is briefly discussed.

Synchronization in Relaxation Oscillator Networks with Conduction Delays

2001 ◽  
Vol 13 (5) ◽  
pp. 1003-1021 ◽  
Author(s):  
Jeffrey J. Fox ◽  
Ciriyam Jayaprakash ◽  
DeLiang Wang ◽  
Shannon R. Campbell
Keyword(s):  
Numerical Simulations ◽  
Coupled Oscillators ◽  
Initial Conditions ◽  
Relaxation Oscillator ◽  
Phase Lag ◽  
Relaxation Oscillators ◽  
Oscillator Networks ◽  
Coupled Networks ◽  
Parameter Values ◽  
Zero Phase

We study locally coupled networks of relaxation oscillators with excitatory connections and conduction delays and propose a mechanism for achieving zero phase-lag synchrony. Our mechanism is based on the observation that different rates of motion along different nullclines of the system can lead to synchrony in the presence of conduction delays. We analyze the system of two coupled oscillators and derive phase compression rates. This analysis indicates how to choose nullclines for individual relaxation oscillators in order to induce rapid synchrony. The numerical simulations demonstrate that our analytical results extend to locally coupled networks with conduction delays and that these networks can attain rapid synchrony with appropriately chosen nullclines and initial conditions. The robustness of the proposed mechanism is verified with respect to different nullclines, variations in parameter values, and initial conditions.

scholarly journals Evidence for a Coupled Oscillator Model of Endocrine Ultradian Rhythms

2018 ◽  
Vol 33 (5) ◽  
pp. 475-496 ◽  
Author(s):  
Azure D. Grant ◽  
Kathryn Wilsterman ◽  
Benjamin L. Smarr ◽  
Lance J. Kriegsfeld
Keyword(s):  
Body Temperature ◽  
Coupled Oscillators ◽  
Endocrine System ◽  
High Temporal Resolution ◽  
Ultradian Rhythms ◽  
Coupled Oscillator ◽  
Long Period ◽  
Temporal Structures ◽  
Oscillator Network ◽  
Coupled Oscillator Model

Whereas long-period temporal structures in endocrine dynamics have been well studied, endocrine rhythms on the scale of hours are relatively unexplored. The study of these ultradian rhythms (URs) has remained nascent, in part, because a theoretical framework unifying ultradian patterns across systems has not been established. The present overview proposes a conceptual coupled oscillator network model of URs in which oscillating hormonal outputs, or nodes, are connected by edges representing the strength of node-node coupling. We propose that variable-strength coupling exists both within and across classic hormonal axes. Because coupled oscillators synchronize, such a model implies that changes across hormonal systems could be inferred by surveying accessible nodes in the network. This implication would at once simplify the study of URs and open new avenues of exploration into conditions affecting coupling. In support of this proposed framework, we review mammalian evidence for (1) URs of the gut-brain axis and the hypothalamo-pituitary-thyroid, -adrenal, and -gonadal axes, (2) UR coupling within and across these axes; and (3) the relation of these URs to body temperature. URs across these systems exhibit behavior broadly consistent with a coupled oscillator network, maintaining both consistent URs and coupling within and across axes. This model may aid the exploration of mammalian physiology at high temporal resolution and improve the understanding of endocrine system dynamics within individuals.

Delay stabilization of periodic orbits in coupled oscillator systems

2010 ◽  
Vol 368 (1911) ◽  
pp. 319-341 ◽  
Author(s):  
B. Fiedler ◽  
V. Flunkert ◽  
P. Hövel ◽  
E. Schöll
Keyword(s):  
Normal Form ◽  
Numerical Simulations ◽  
Periodic Orbits ◽  
Coupled Oscillators ◽  
Coupled Oscillator ◽  
Non Invasive ◽  
Coupling Parameters ◽  
Necessary And Sufficient ◽  
Time Delayed Feedback ◽  
Coupled Oscillator Systems

We study diffusively coupled oscillators in Hopf normal form. By introducing a non-invasive delay coupling, we are able to stabilize the inherently unstable anti-phase orbits. For the super- and subcritical cases, we state a condition on the oscillator’s nonlinearity that is necessary and sufficient to find coupling parameters for successful stabilization. We prove these conditions and review previous results on the stabilization of odd-number orbits by time-delayed feedback. Finally, we illustrate the results with numerical simulations.

Asynchronous states in networks of pulse-coupled oscillators

1993 ◽  
Vol 48 (2) ◽  
pp. 1483-1490 ◽  
Author(s):  
L. F. Abbott ◽  
Carl van Vreeswijk
Keyword(s):  
Coupled Oscillators ◽  
Pulse Coupled Oscillators

Revisiting an old concept: the coupled oscillator model for VCD. Part 2: implications of the generalised coupled oscillator mechanism for the VCD robustness concept

2016 ◽  
Vol 18 (31) ◽  
pp. 21213-21225 ◽  
Author(s):  
Valentin Paul Nicu
Keyword(s):  
Relative Orientation ◽  
Oscillator Model ◽  
Coupled Oscillator ◽  
Displacement Vectors ◽  
The Stability ◽  
Coupled Oscillator Model

The generalised coupled oscillator (GCO) mechanism implies that the stability of the computed VCD sign should be assigned by monitoring the uncertainties in the relative orientation of the GCO fragments and in the nuclear displacement vectors, i.e. not the magnitude of the dissymmetry factor.

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