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Precise Self-tuning of Spiking Patterns in Coupled NeuronalOscillators

Published online by Cambridge University Press:  12 December 2012

I.Y. Tyukin  and
V.B. Kazantsev
I.Y. Tyukin*
Affiliation:
Department of Mathematics, University of Leicester, University Road, LE1 7RH, UK Department of Automation and Control Processes, Saint-Petersburg State Electrotechnical University Prof. Popova str. 5, 197376, Russia
V.B. Kazantsev
Affiliation:
Department of Nonlinear Dynamics, Institute of Applied Physics of RAS Nizhny Novgorod, Russia Department of Neurodynamics and Neurobiology, University of Nizhny Novgorod Nizhny Novgorod, Russia
*
⋆ Corresponding author. E-mail: I.Tyukin@le.ac.uk
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Abstract

In this work we discuss and analyze spiking patterns in a generic mathematical model oftwo coupled non-identical nonlinear oscillators supplied with a spike-timing dependentplasticity (STDP) mechanism. Spiking patterns in the system are shown to converge to aphase-locked state in a broad range of parameters. Precision of the phase locking, i.e.the amplitude of relative phase deviations from a given reference, depends on the naturalfrequencies of oscillators and, additionally, on parameters of the STDP law. Thesedeviations can be optimized by appropriate tuning of gains (i.e. sensitivity tospike-timing mismatches) of the STDP mechanisms. The deviations, however, can not be madearbitrarily small neither by mere tuning of STDP gains nor by adjusting synaptic weights.Thus if accurate phase-locking in the system is required then an additional tuningmechanism is generally needed. We found that adding a very simple adaptation dynamics inthe form of slow fluctuations of the base line in the STDP mechanism enables accuratephase tuning in the system with arbitrary high precision. The scheme applies to systems inwhich individual oscillators operate in the oscillatory mode. If the dynamics ofoscillators becomes bistable then relative phase may fail to converge to a given valuegiving rise to the emergence of complex spiking sequences.

Keywords

nonlinear phase oscillatorsspike-timing dependent plasticityadaptive controlnonlinear parametrizationconvergenceweak attractorsneural oscillators
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 6: Biological oscillations , 2012 , pp. 67 - 94
Copyright
© EDP Sciences, 2012

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