# Predicting synchrony in heterogeneous pulse coupled oscillators.

@article{Talathi2009PredictingSI, title={Predicting synchrony in heterogeneous pulse coupled oscillators.}, author={Sachin S. Talathi and Dong-Uk Hwang and Abraham Miliotis and Paul R. Carney and William L. Ditto}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2009}, volume={80 2 Pt 1}, pages={ 021908 } }

Pulse coupled oscillators (PCOs) represent an ubiquitous model for a number of physical and biological systems. Phase response curves (PRCs) provide a general mathematical framework to analyze patterns of synchrony generated within these models. A general theoretical approach to account for the nonlinear contributions from higher-order PRCs in the generation of synchronous patterns by the PCOs is still lacking. Here, by considering a prototypical example of a PCO network, i.e., two synaptically…

## 17 Citations

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A general theoretical framework using spike time response curves (STRC’s) to study patterns of synchrony in a simple network of two unidirectionally coupled interneurons interacting through a shunting synapse is developed and an approximate discrete map is derived to analyze the dynamics of synchronous states in the UCI network by taking into account the nonlinear contributions of the higher order STRC terms.

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- BiologyPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

It is shown that a recently developed tool, the functional phase resetting curve (fPRC), provides a serendipitous benefit: it allows incorporation of nonoscillatory elements into systems of oscillators where PRT can be applied.

### Inclusion of noise in iterated firing time maps based on the phase response curve.

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- 2010

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### Three synaptic components contributing to robust network synchronization.

- BiologyPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

The relationship between the robustness of the synchrony and the parameters, search for the optimal parameter set for the robust network synchronization of a certain frequency band, and demonstrate the key role of the voltage-dependent properties of synaptic currents in robust or stable synchronization are discussed.

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- 2011

An algorithm to control synchrony between two periodically firing neurons is described, which is a low impact stimulation method that brings the neurons toward the desired level of synchrony over the course of several neuron firing periods.

### Controlling spike timing and synchrony in oscillatory neurons.

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