Math. Model. Nat. Phenom.
Volume 7, Number 6, 2012Biological oscillations
|Page(s)||67 - 94|
|Published online||12 December 2012|
Precise Self-tuning of Spiking Patterns in Coupled Neuronal Oscillators
1 Department of Mathematics, University
of Leicester, University Road, LE1 7RH,
2 Department of Automation and Control Processes, Saint-Petersburg State Electrotechnical University Prof. Popova str. 5, 197376, Russia
3 Department of Nonlinear Dynamics, Institute of Applied Physics of RAS Nizhny Novgorod, Russia
4 Department of Neurodynamics and Neurobiology, University of Nizhny Novgorod Nizhny Novgorod, Russia
⋆ Corresponding author. E-mail: I.Tyukin@le.ac.uk
In this work we discuss and analyze spiking patterns in a generic mathematical model of two coupled non-identical nonlinear oscillators supplied with a spike-timing dependent plasticity (STDP) mechanism. Spiking patterns in the system are shown to converge to a phase-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 natural frequencies of oscillators and, additionally, on parameters of the STDP law. These deviations can be optimized by appropriate tuning of gains (i.e. sensitivity to spike-timing mismatches) of the STDP mechanisms. The deviations, however, can not be made arbitrarily 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 tuning mechanism is generally needed. We found that adding a very simple adaptation dynamics in the form of slow fluctuations of the base line in the STDP mechanism enables accurate phase tuning in the system with arbitrary high precision. The scheme applies to systems in which individual oscillators operate in the oscillatory mode. If the dynamics of oscillators becomes bistable then relative phase may fail to converge to a given value giving rise to the emergence of complex spiking sequences.
Mathematics Subject Classification: 92B25 / 92C20 / 37N25 / 37M20
Key words: nonlinear phase oscillators / spike-timing dependent plasticity / adaptive control / nonlinear parametrization / convergence / weak attractors / neural oscillators
© EDP Sciences, 2012
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