Asymptotic periodicity in networks of degrade-and-fire oscillators

@article{Blumenthal2015AsymptoticPI,
  title={Asymptotic periodicity in networks of degrade-and-fire oscillators},
  author={Alex Blumenthal and Bastien Fernandez},
  journal={Physica D: Nonlinear Phenomena},
  year={2015},
  volume={323},
  pages={49-56}
}
2 Citations

Figures from this paper

Revisiting asymptotic periodicity in networks of degrade-and-fire oscillators
  • B. Fernandez
  • Mathematics
    The European Physical Journal Special Topics
  • 2018
TLDR
This example shows in particular that the updated conditions for asymptotic periodicity are optimal and provides a novel instance of direct impact of the topology of interactions in the global dynamics of a collective system.

References

SHOWING 1-10 OF 21 REFERENCES
Population Dynamics of Globally Coupled Degrade-and-Fire Oscillators
This paper reports the analysis of a model of pulse-coupled oscillators with global inhibitory coupling, inspired by experiments on colonies of bacteria-embedded synthetic genetic circuits.
Typical trajectories of coupled degrade-and-fire oscillators: from dispersed populations to massive clustering
TLDR
A sharp transition is proved to exist that separates a weak coupling regime of unclustered populations from a strong coupling phase where clusters of extensive size are formed, and it is shown that with positive probability, the number of asymptotic clusters remains bounded, provided that the coupling strength is sufficiently large.
Corepressive interaction and clustering of degrade-and-fire oscillators.
TLDR
This work studies the synchronization of DF oscillators coupled through a common repressor field and finds that in the thermodynamic limit a phase transition occurs at a certain coupling strength from the weakly clustered regime with only microscopic clusters to a strongly clustered regime where at least one giant cluster has to be present.
Synchronization of degrade-and-fire oscillations via a common activator.
TLDR
This work examines an experimentally motivated stochastic model for coupled degrade-and-fire gene oscillators, where a core delayed negative feedback establishes oscillations within each cell, and a shared delayed positive feedback couples all cells.
Similar NonLeaky Integrate-and-Fire Neurons with Instantaneous Couplings Always Synchronize
TLDR
It is proved that generically the dynamics of pulse-coupled integrate-and-fire neurons becomes fully synchronous for any initial conditions if the intrinsic frequencies, the thresholds, and the couplings are not too different.
Delay-induced degrade-and-fire oscillations in small genetic circuits.
TLDR
Deterministic and stochastic modeling is used to investigate how a small time delay in regulatory networks can lead to strongly nonlinear oscillations that can be characterized by "degrade-and-fire" dynamics.
Synchronization of pulse-coupled biological oscillators
A simple model for synchronous firing of biological oscillators based on Peskin's model of the cardiac pacemaker (Mathematical aspects of heart physiology, Courant Institute of Mathematical Sciences,
Symmetry Groupoids and Patterns of Synchrony in Coupled Cell Networks
A coupled cell system is a network of dynamical systems, or "cells," coupled together. Such systems can be represented schematically by a directed graph whose nodes correspond to cells and whose
Entrainment of a Population of Synthetic Genetic Oscillators
TLDR
This work simultaneously tracked the phases of hundreds of synthetic genetic oscillators relative to a common external stimulus to map the entrainment regions predicted by a detailed model of the clock.
Synchronization induced by temporal delays in pulse-coupled oscillators.
TLDR
In large ensembles of globally coupled oscillators the delayed interaction leads to new collective phenomena like synchronization in multistable clusters of common phases for inhibitory coupling; for excitatory coupling a mechanism of emerging and decaying synchronized clusters prevails.
...
1
2
3
...