New type of excitatory pulse coupling of chemical oscillators via inhibitor

Proskurkin, Ivan S.; Vanag, Vladimir K.

doi:10.1039/c5cp02098k

Cited by 16 publications

(10 citation statements)

References 30 publications

(61 reference statements)

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“…However, there is a very easy criterion reflecting this structure, which is the presence of regions with slope < -1 in the PRC. PRCs possessing this property have been experimentally measured here for the electronic oscillator and by other authors for chemical oscillators [71,72] and cardiac cells [73][74][75]. As for neurons, PRCs with steep falling parts have been observed [59], but there is no data whether their slope can be less than -1 or not.…”

Section: Discussionmentioning

confidence: 65%

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: 65%

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

et al. 2015

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“…In the antenna unit, which consists of four MRs as well (k = 1-4), we also use unidirectional coupling on the ring, but with ''negative'' light pulses (a pulsed cut-off of the steady illumination). 30 To transform the oscillatory BZ reaction into an excitable steady state (SS), we illuminate it continuously with light intensity I SS = 0.78 klx.…”

Section: Methodsmentioning

confidence: 99%

“…We call such excitatory pulses ''negative''. 30 In Fig. 3(b), we demonstrate the action of the ''negative'' pulse induced by a sharp spike in cell #1 (blue curve) on the neighboring cell #2 (red curve).…”

Section: A Antennamentioning

confidence: 95%

Experimental verification of an opto-chemical “neurocomputer”

Proskurkin

Smelov

Vanag

2020

Phys. Chem. Chem. Phys.

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“…, heart beat rhythm 5,6 , human walking motion 7,8 , circadian clock 9,10 , oscillation in chemical reactions 11,12 and earthquake dynamics. 13 In short, systems with dynamical elements that compose of spontaneous rhythms are used for Phase Response Curves (PRCs).…”

Section: -4mentioning

confidence: 99%

“…Oscillating systems is in everywhere we encounter without realizing in everyday life. Some examples of oscillating systems from biology, chemistry, physics and engineering are single nerve cell that generates action potential 1-4 , heart beat rhythm 5,6 , human walking motion 7,8 , circadian clock 9,10 , oscillation in chemical reactions 11,12 and earthquake dynamics. 13 In short, systems with dynamical elements that compose of spontaneous rhythms are used for Phase Response Curves (PRCs).…”

Section: Introductionmentioning

confidence: 99%

Examining phase response curve of nerve cell by using three different methods

Eskalen

Özğan

2018

International Journal of Chemistry and Technology

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Rhythmic motion is observed in a variety of different field including physical, chemical and biological systems. Neural system, that consists of billions of neurons are also exhibited periodic motion. Phase Response Curves (PRCs); act like a bridge between, a single neuron and neural network; briefly measure change in period of oscillation by giving perturbation at different points of oscillation. PRCs can determined from measurements of electrical activities of neurons by experimental methods or theoretically derived from three different methods. As far as we know from the literature, these three different methods have never been used at the same time before. The main purpose of this computational study is to the obtain Phase Response Curve by three different methods and compare them in terms of simulation times and peak to baseline ratio. First, the kinds of excitability of neurons, the types of Phase Response Curve and peak to baseline ratio are mentioned. After then, these three different methods to obtain PRC are explained deeply. At a final step, Phase Response Curves are obtained from three theoretical methods and compared regarding to peak to baseline ratio, simulation time and applicability.

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New type of excitatory pulse coupling of chemical oscillators via inhibitor

Cited by 16 publications

References 30 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

Experimental verification of an opto-chemical “neurocomputer”

Examining phase response curve of nerve cell by using three different methods

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