Dynamical structure underlying inverse stochastic resonance and its implications

Uzuntarla, Muhammet; Cressman, John R.; Özer, Mahmut; Barreto, Ernest

doi:10.1103/physreve.88.042712

Cited by 54 publications

(49 citation statements)

References 40 publications

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“…It was often found that with close to c , spiking was terminated completely after one or a few spikes. Similar results were obtained when (a) the noise was conductance-based, as opposed to current-based, as is more appropriate for synaptic inputs, (b) current-based noise was introduced (turned-on) at a random chosen time point ), (c) channel noise was used instead of current noise (Schmerl and McDonnell 2013;Uzuntarla et al 2013), and (d) coloured noise instead of white Gaussian noise was used (Guo 2011). These variations established that the occurrence of minima in firing rate with increasing noise when is close to c is robust to significant model changes.…”

Section: Hodgkin-huxley System Of Odessupporting

confidence: 63%

“…In the case of many types of neuron (and also cardiac cells) the rhythmic behaviour is called pacemaker activity and can be driven or intrinsic. The inhibiting effect of noise on such rhythmic activity was first explored experimentally in the squid axon (Paydarfar et al 2006) and theoretically in Hodgkin-Huxley (HH) or related models of ordinary differential equations Gutkin et al 2009;Guo 2011;Tuckwell and Jost 2012;Schmerl and McDonnell 2013;Uzuntarla et al 2013) (the specific contributions of these papers are explained below) and the partial differential equation HH model (Tuckwell andJost 2010, 2011). A brief summary will be given of the results for some of the inhibitory effects of white noise in the HH systems.…”

Section: Comparison Of Reviewed Models With Stochastic Facilitationmentioning

confidence: 99%

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A review of methods for identifying stochastic resonance in simulations of single neuron models

McDonnell

Iannella

et al. 2015

Network: Computation in Neural Systems

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Stochastic resonance (SR) is said to be observed when the presence of noise in a nonlinear system enables an output signal from the system to better represent some feature of an input signal than it does in the absence of noise. The effect has been observed in models of individual neurons, and in experiments performed on real neural systems. Despite the ubiquity of biophysical sources of stochastic noise in the nervous system, however, it has not yet been established whether neuronal computation mechanisms involved in performance of specific functions such as perception or learning might exploit such noise as an integral component, such that removal of the noise would diminish performance of these functions. In this paper we revisit the methods used to demonstrate stochastic resonance in models of single neurons. This includes a previously unreported observation in a multicompartmental model of a CA1-pyramidal cell. We also discuss, as a contrast to these classical studies, a form of 'stochastic facilitation', known as inverse stochastic resonance. We draw on the reviewed examples to argue why new approaches to studying 'stochastic facilitation' in neural systems need to be developed.

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Section: Hodgkin-huxley System Of Odessupporting

confidence: 63%

Section: Comparison Of Reviewed Models With Stochastic Facilitationmentioning

confidence: 99%

A review of methods for identifying stochastic resonance in simulations of single neuron models

McDonnell

Iannella

et al. 2015

Network: Computation in Neural Systems

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“…During ISR, when the intensity of the (weak) noise amplitude is increased, it will first strongly inhibit the spiking activity and decrease the mean number of spikes to a minimal value, but a further increase in the noise amplitude will increase the mean number of spikes again, even above what is observed in the noise-free case. Mathematically, ISR has not been extensively studied as compared to other resonance phenomena; see [50][51][52][53], and it was recently confirmed experimentally in [54].…”

Section: Introductionmentioning

confidence: 99%

Coherent neural oscillations induced by weak synaptic noise

Yamakou

Jost

2018

Nonlinear Dyn

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We analyze the effect of synaptic noise on the dynamics of the FitzHugh-Nagumo (FHN) neuron model. In our deterministic parameter regime, a limit cycle solution cannot emerge through a singular Hopf bifurcation, but such a limit cycle can nevertheless arise as a stochastic effect, as a consequence of weak synaptic noise in a regime of strong timescale separation (ε → 0) between the slow and fast variables of the model. We investigate the mechanism behind this phenomenon, known as self-induced stochastic resonance (SISR) (Muratov et al. in Physica D 210:227-240, 2005), by using multiple-time perturbation techniques and by analyzing the escape mechanism of the random trajectories from the stable manifolds of the model equation. Even though SISR occurs only in the limit as the singular parameter ε → 0, decreasing ε does not increase the coherence of the oscillations in the FHN model, but rather increases the interval of the noise amplitude σ for which coherence occurs. This is in contrast to the dynamical system studied in Mura- 2005). Moreover, the phenomenon is robust under parameter tuning. Numerical simulations exhibit the results predicted by the theoretical analysis. In fact, our analysis together with that in Yamakou and Jost (Weak noise-induced transitions with inhibition and modulation of neural oscillations, 2017) reveals that the FHN model can support different stochastic resonance phenomena. While it had been known (Pikovsky and Kurths in Phys Rev Lett 78:775-778, 1997) that coherence resonance can occur when the slow variable is subjected to noise, we show that, when noise is added to the fast variable, two other types, inverse stochastic resonance and SISR, may emerge in the same weak noise limit and that the transition between these phenomena can be induced by varying a simple parameter.

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“…Other authors considered the Morris-Lecar model neuron [17], and showed that ISR can emerge as a consequence of unreliable spike transmission [18]. In another work [19], the authors studied the phenomenon of ISR in the Hodgkin-Huxley (HH) neuron based on biophysically realistic ion channel noise. These authors also clarified the dynamical structure that underlies ISR.…”

Section: Introductionmentioning

confidence: 99%

Inverse stochastic resonance in networks of spiking neurons

2017

Self Cite

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Inverse Stochastic Resonance (ISR) is a phenomenon in which the average spiking rate of a neuron exhibits a minimum with respect to noise. ISR has been studied in individual neurons, but here, we investigate ISR in scale-free networks, where the average spiking rate is calculated over the neuronal population. We use Hodgkin-Huxley model neurons with channel noise (i.e., stochastic gating variable dynamics), and the network connectivity is implemented via electrical or chemical connections (i.e., gap junctions or excitatory/inhibitory synapses). We find that the emergence of ISR depends on the interplay between each neuron’s intrinsic dynamical structure, channel noise, and network inputs, where the latter in turn depend on network structure parameters. We observe that with weak gap junction or excitatory synaptic coupling, network heterogeneity and sparseness tend to favor the emergence of ISR. With inhibitory coupling, ISR is quite robust. We also identify dynamical mechanisms that underlie various features of this ISR behavior. Our results suggest possible ways of experimentally observing ISR in actual neuronal systems.

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Dynamical structure underlying inverse stochastic resonance and its implications

Cited by 54 publications

References 40 publications

A review of methods for identifying stochastic resonance in simulations of single neuron models

A review of methods for identifying stochastic resonance in simulations of single neuron models

Coherent neural oscillations induced by weak synaptic noise

Inverse stochastic resonance in networks of spiking neurons

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