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Section BRAIN-COMPUTER INTERFACES, COGNITIVE NAVIGATION WORKSHOP AND NEUROENGINEERING
The Dependence on Noise of STDP-Driven Synchronization at Neural Network
S.A. Lobov1*, M.O. Zhuravlev1, V.A.Makarov1'2, V.B. Kazantsev1
1 Lobachevsky State University of Nizhny Novgorod, Gagarin Ave. 23, 603950 Nizhny Novgorod, Russia;
2 Instituto de Matemática Interdisciplinar, Applied Mathematics Dept., Universidad Complutense de Madrid,Spain. * Presenting e-mail: lobov@neuro.nnov.ru
Synchronization in neuron networks is known to play an important role in brain information processing [1]. Earlier we showed the synchronization of neural network response on spatially localized periodic stimulation [2]. Because of spike-timing-dependent synaptic plasticity (STDP) the steady-state spatial pattern of the weights rearranged and these changes underlay the synchronization phenomenon. Here we investigate the role of neural noise in the synchronization.
The network consisted of synaptically coupled spiking neurons simulated by Izhikevich's model [3]. 400 excitory and 100 inhibitory neurons were used. Short term (Tsodiks-Markram model, [4]) and long term plasticity (STDP) took place. Each neuron was exposed by a mutually independent and uncorrelated Gaussian white noise -V2D with variance D <£(t) = 0 (^(t(t ) = St .S(t -f) , '
The stimulus was introduced to the network by activation of an arbitrary chosen group containing one inhibitory and five excitatory neurons located in the same small network area. Each stimulus made all the neurons from the chosen group to fire, which in turn could produce population burst of spikes. Frequency of stimulation was 10 Hz. If the synchronization appeared all stimuli led to bursts generation, so frequency of bursts equal to 10 Hz was a criterion of the synchronization.
We varied noise variance D and registered time required for network synchronization. For illustration purpose we introduced the synchronization index which was equal to 1/t, where t - time of stimulation to synchronization. The Fig. 1A shows examples of different evolutions of bursts frequency in the condition of various noise variance. When noise was small there were no bursts and accordingly no synchronization (Fig. 1A, 1). At increase of noise variance some unstable synchronization appeared (Fig. 1A, 2). In the conditions of middle noise the perfect synchronization took place (Fig. 1A, 3). At further increase of noise variance unstable synchronization could appear again (Fig. 1A, 4). Finally in the conditions of big noise there was the lack of synchronization (Fig. 1A, 5). The Fig. 1B summarizes the dependence of the synchronization on level of neural noise.
It should be noted that the transition from asynchronous to synchronous dynamic behavior in the system is carried out through the intermittent behavior, which is reflected in the alternation of synchronous dynamic areas with areas where there is no synchronization (Fig.1A 2, 4 "unstable synchronization") while all control parameters of the system are constant. This type of transition from synchronization to the asynchronous state is characteristic of the wide range of non-linear dynamical systems [5, 6]. The supercritical parameter in the system appears the noise variance, which is responsible for the existence of intermittent behavior and its defining characteristics.
Fig.1. The dependence of the network synchronization on neural noise variance. A) examples of different evolutions of bursts frequency: 1) the absence of bursts and accordingly lack of synchronization in the conditions of small noise; 2) unstable synchronization at increase of noise level; 3) the synchronization in the conditions of middle noise; 4) unstable synchronization at further increase of noise variance; 5) the lack of synchronization in the conditions of big noise. B) The dependence of the synchronization index on level of neural noise
Section BRAIN-COMPUTER INTERFACES, COGNITIVE NAVIGATION WORKSHOP AND NEUROENGINEERING
Acknowledgements
This work was supported by the Russian Science Foundation under project 15-12-10018. References
1. G. Buzsaki, Rhythms of the Brain (Oxford University Press, 2009).
2. S. Lobov, A. Simonov, I. Kastalskiy V. Kazantsev Network response synchronization enhanced by synaptic plasticity. Eur. Phys. J. Special Topics, 225 1 (2016) 29-39 DOI: http://dx.doi.org/10.1140/epjst/e2016-02614-y
3. Izhikevich E. M. "Simple model of spiking neurons," IEEE Trans. Neural Networks, vol. 14, pp. 1569-1572, Nov. 2003.
4. Tsodyks M., Pawelzik K., Markram H.: Neural network with dynamic synapses. Neural Computations 10: p. 821835. 1998.
5. Berge P, Pomeau Y, Vidal C. Order within chaos. New York: John Wiley and Sons; 1984
6. H. G., Schuster, Deterministic Chaos: An Introduction (Physik, Weinheim, 1984).
Synchronization of Two Coupled Electronic Neurons via Memristor
S.A Gerasimova*, A.N. Mikhaylov, D.S. Korolev, A.I. Belov, I.N. Antonov, O.N. Gorshkov, V.B. Kazantsev
Lobachevsky University, Nizhny Novgorod, Russia. * Presenting e-mail: gerasimova@neuro.nnov.ru
Design of electronic neuron networks capable to reproduce brain functions in silico is one of the most intriguing challenges in modern science and engineering. Such systems would permit to develop new generation of information processing technologies based on brain computation principles. Another interesting application is to make an interface between electronic circuits and living neurons for biomedicine. The electronic circuits should resemble all dynamical regimes of nerve pulse generation in single neurons. In the network design, the crucial point is synaptic coupling between neurons providing reliable signal transmission. Moreover, the coupling strength can be variable depending on the ongoing neuron activity, what is called synaptic plasticity.
In this work, the dynamics of two electronic neuron oscillators coupled via memristor has been investigated. Each neuron is implemented as pulse signal generator based on the FiteHugh-Nagumo equations. This model provides a qualitative description of the main neurons' characteristics including the excitable and self-oscillatory dynamics. Different neuron-like signals (single pulse, transients, self-oscillations) can be observed by changing threshold parameter. Memristor is realized in a simple metal-oxide-metal nanostructure demonstrating reproducible resistive switching effect [1].
After testing and tuning of the master and slave neuron oscillators their coupling by memristor was implemented. The output signal from the master neuron was conveyed to input of memristor. Output signal from memristor sent to the input of the slave neuron. Such unidirectional signal transmission implements the functionality of excitatory synaptic coupling.
Such model mimics the interaction between synaptically coupled brain neurons, where the memristor imitates neuron axon. The resistance can be continuously varied, and such analog variation of resistance provides a useful model of key features of the biological synapse, and memristor as synapses in neuromorphic circuits can model synaptic plasticity. The synaptic connection is modelled by output signal from memristor. It is experimentally demonstrated that such connection can provide forced synchronization with locking ratios 1:1.
Acknowledgements
The study is supported by the Russian Science Foundation (grant 16-19-00144). References
1. A.N. Mikhaylov, A.I. Belov, D.V. Guseinov et al., Mat. Sci. Eng. B, 2015, 194, 48-54.
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