Dynamics of two neuronlike elements with inhibitory feedback

Shchapin, Dmitry

doi:10.1134/s1064226909020089

Cited by 14 publications

(12 citation statements)

References 20 publications

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“…In view of the arbitrarily high dimensional critical manifolds of the RS solution, which were observed in this paper, it seems to be worth studying such computational abilities for an oscillator with delayed pulsatile feedback. An electronic implementation of such systems is relatively uncomplicated [7,42,64].…”

Section: Discussionmentioning

confidence: 99%

Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback

et al. 2015

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Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator reaches a specific state, it emits a pulse, which returns after propagating through a delay line. The impact of an incoming pulse is described by the oscillator's phase reset curve (PRC). In such a system we discover an unexpected phenomenon: for a sufficiently steep slope of the PRC, a periodic regular spiking solution bifurcates with several multipliers crossing the unit circle at the same parameter value. The number of such critical multipliers increases linearly with the delay and thus may be arbitrary large. This bifurcation is accompanied by the emergence of numerous "jittering" regimes with nonequal interspike intervals (ISIs). Each of these regimes corresponds to a periodic solution of the system with a period roughly proportional to the delay. The number of different "jittering" solutions emerging at the bifurcation point increases exponentially with the delay. We describe the combinatorial mechanism that underlies the emergence of such a variety of solutions. In particular, we show how a periodic solution exhibiting several distinct ISIs can imply the existence of multiple other solutions obtained by rearranging of these ISIs. We show that the theoretical results for phase oscillators accurately predict the behavior of an experimentally implemented electronic oscillator with pulsatile feedback.

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Section: Discussionmentioning

confidence: 99%

Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback

et al. 2015

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“…The experimental setup is described in detail in the Supplemental materials. It was based on the electronic FitzHugh-Nagumo oscillator [53,54]. When the output voltage exceeds a threshold value, a spike is produced and sent to a delay line.…”

mentioning

confidence: 99%

Mode Hopping in Oscillating Systems with Stochastic Delays

2020

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“…In order to simulate neural dynamics, we explored two FHN neuron generators with cubic nonlinearity constructed using diodes [ 7 , 22 ]. The dynamics of the presynaptic FHN neuron was modeled by the normalized equations obtained with the Kirchhoff law [ 21 ] as follows:

where u 1 is the membrane potential of the presynaptic neuron, ν 1 is the “recovery” variable related to the ion current, f ( u 1 ) = u 1

u 1 3 /3 is the cubic nonlinearity, I 1 is the depolarization parameter characterizing the excitation threshold, and ε is a small coefficient.…”

Section: Methodsmentioning

confidence: 99%

“…The dynamics of the presynaptic FHN neuron was modeled by the normalized equations obtained with the Kirchhoff law [ 21 ] as follows:

where u 1 is the membrane potential of the presynaptic neuron, ν 1 is the “recovery” variable related to the ion current, f ( u 1 ) = u 1

u 1 3 /3 is the cubic nonlinearity, I 1 is the depolarization parameter characterizing the excitation threshold, and ε is a small coefficient. If u 1 < 0, the function g ( u 1 ) = αu 1 , and if u 1 ≥ 0, g ( u 1 ) = βu 1 ( α , β being the parameters that control, respectively, the shape and location of the ν -nullcline [ 22 ]).…”

Section: Methodsmentioning

confidence: 99%

“…The analog electronic FHN neuron consisted of the following blocks: an oscillatory contour unit, a nonlinearity unit, and an amplifier unit (see Figure 1 b). The detailed design of this device is described in [ 7 , 22 ]. The FHN neural generator demonstrates the main qualitative features of neurodynamics: the presence of an excitability threshold and the existence of resting and spiking regimes.…”

Section: Methodsmentioning

confidence: 99%

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Stochastic Memristive Interface for Neural Signal Processing

Gerasimova

Belov

Королев

et al. 2021

Sensors

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We propose a memristive interface consisting of two FitzHugh–Nagumo electronic neurons connected via a metal–oxide (Au/Zr/ZrO2(Y)/TiN/Ti) memristive synaptic device. We create a hardware–software complex based on a commercial data acquisition system, which records a signal generated by a presynaptic electronic neuron and transmits it to a postsynaptic neuron through the memristive device. We demonstrate, numerically and experimentally, complex dynamics, including chaos and different types of neural synchronization. The main advantages of our system over similar devices are its simplicity and real-time performance. A change in the amplitude of the presynaptic neurogenerator leads to the potentiation of the memristive device due to the self-tuning of its parameters. This provides an adaptive modulation of the postsynaptic neuron output. The developed memristive interface, due to its stochastic nature, simulates a real synaptic connection, which is very promising for neuroprosthetic applications.

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Dynamics of two neuronlike elements with inhibitory feedback

Cited by 14 publications

References 20 publications

Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback

Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback

Mode Hopping in Oscillating Systems with Stochastic Delays

Stochastic Memristive Interface for Neural Signal Processing

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