Volume 112, Number 3, November 2015
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||18 November 2015|
Mechanism of quasi-periodic lag jitter in bursting rhythms by a neuronal network
1 Departamento de Matemática Aplicada and IUMA, University of Zaragoza - E-50009 Zaragoza, Spain
2 CODY and GME, University of Zaragoza - E-50009 Zaragoza, Spain
3 Centro Universitario de la Defensa - E-50090 Zaragoza, Spain
4 Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University Atlanta, GA, USA
5 Institute for Information Technologies, Mathematics and Mechanics, Lobachevsky State University of Nizhni Novgorod - Nizhni Novgorod, Russia
Received: 15 September 2015
Accepted: 30 October 2015
We study a heteroclinic bifurcation leading to the onset of robust phase-lag jittering in bursting rhythms generated by a neuronal circuit. We show that the jitter phenomenon is associated with the occurrence of a stable invariant curve emerging through a torus bifurcation in 2D return maps for phase lags between three constituent bursters. To study biologically plausible and phenomenological models of rhythmic neuronal networks we have further developed parallel computational techniques for parameter continuations of all possible fixed points and invariant curves of such return maps. The method is based on a “fine” brute-force analysis of the large data set generated by the computational techniques.
PACS: 87.19.lj – Neuronal network dynamics / 87.19.ll – Models of single neurons and networks / 87.19.lm – Synchronization in the nervous system
© EPLA, 2015
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