Synchrony and Desynchrony in Integrate-and-Fire Oscillators

Campbell, Shannon R.; Wang, DeLiang L.; Jayaprakash, C.

doi:10.1162/089976699300016160

Cited by 162 publications

(58 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The temporal behavior of the model should also scale up well. Campbell et al (1999) recently showed that time to synchronization in locally connected integrate-and-fire neurons is logarithmically proportional to the network size. Since the dynamic threshold neuron used in the current model is equivalent to integrateand-fire neurons, we expect our model to show similar, manageable temporal scaling behavior as the network size is increased.…”

Section: Discussionmentioning

confidence: 99%

Contour integration and segmentation with self-organized lateral connections

Choe

Miikkulainen

2004

Biological Cybernetics

View full text Add to dashboard Cite

Contour integration in low-level vision is believed to occur based on lateral interaction between neurons with similar orientation tuning. How such interactions could arise in the brain has been an open question. Our model suggests that the interactions can be learned through input-driven self-organization, i.e. through the same mechanism that underlies many other developmental and functional phenomena in the visual cortex. The model also shows how synchronized firing mediated by these lateral connections can represent the percept of a contour, resulting in performance similar to that of human contour integration. The model further demonstrates that contour integration performance can differ in different parts of the visual field, depending on what kinds of input distributions they receive during development. The model thus grounds an important perceptual phenomenon onto detailed neural mechanisms, so that various structural and functional properties can be measured, and predictions can be made to guide future experiments.

show abstract

Section: Discussionmentioning

confidence: 99%

Contour integration and segmentation with self-organized lateral connections

Choe

Miikkulainen

2004

Biological Cybernetics

View full text Add to dashboard Cite

show abstract

“…[36][37][38][39][40][41][42][43] considered more general networks of excitable coupling on oscillatory elements and [44,45] considered the role of inhibition in synchronizing such networks. A detailed study of the time needed for synchronization was performed in [46]; a general study of the effects of noise on excitable systems is in [47]. Further generalization of Mirollo and Strogatz's work to a population of non-identical pulse-coupled oscillators was considered by Senn and Urbanczik [48], who showed that deterministic networks without leakiness synchronize generically.…”

Section: Previous Work; Motivation For Current Studymentioning

confidence: 99%

Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks

Deville

Peskin

2011

Bull Math Biol

View full text Add to dashboard Cite

We describe and analyze a model for a stochastic pulse-coupled neuronal network with many sources of randomness: random external input, potential synaptic failure, and random connectivity topologies. We show that different classes of network topologies give rise to qualitatively different types of synchrony: uniform (Erdős-Rényi) and "small-world" networks give rise to synchronization phenomena similar to that in "all-to-all" networks (in which there is a sharp onset of synchrony as coupling is increased); in contrast, in "scale-free" networks the dependence of synchrony on coupling strength is smoother. Moreover, we show that in the uniform and small-world cases, the fine details of the network are not important in determining the synchronization properties; this depends only on the mean connectivity. In marked contrast, for scale-free networks, the dynamics are significantly affected by the fine details of the network; in particular, they are significantly affected by the local neighborhoods of the "hubs" in the network.

show abstract

“…Repeating integrate-and-fire behavior between a constant threshold and a periodic base signal, the BN can exhibit various chaotic/periodic phenomena. On the other hand, integrate-andfire neuron models have been applied to many engineering systems including associative memories [2], image processors [7], and communication systems [4,8]. In the spiking neuron models (incl.…”

Section: Introductionmentioning

confidence: 99%

A simple integrate-and-fire system and various super-stable periodic orbits

Takahashi

Saito

2018

NOLTA

View full text Add to dashboard Cite

This paper studies super-stable periodic orbits and related phenomena in a simple switched dynamical system. The system repeats integrate-and-fire behavior between a constant threshold and a periodic base signal. The base signal consists of two components: the fundamental and higher frequency triangular signals. First, we demonstrate "chaos + chaos = order" such that the system exhibits chaos if the base signal is either of the two components whereas the system exhibits a super-stable periodic orbit if the base signal consists of both components. This phenomenon is confirmed experimentally and is explained theoretically. Second, we extract two key parameters and show that the system can exhibit a variety of super-stable periodic orbits. Applying a mapping procedure, existence regions of basic super-stable periodic orbits are calculated precisely.

show abstract

Synchrony and Desynchrony in Integrate-and-Fire Oscillators

Cited by 162 publications

References 21 publications

Contour integration and segmentation with self-organized lateral connections

Contour integration and segmentation with self-organized lateral connections

Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks

A simple integrate-and-fire system and various super-stable periodic orbits

Contact Info

Product

Resources

About