Noise-induced torus bursting in the stochastic Hindmarsh-Rose neuron model

Ryashko, Lev; Slepukhina, Evdokia

doi:10.1103/physreve.96.032212

Cited by 41 publications

(10 citation statements)

References 37 publications

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“…This result confirms the bispectral analysis of some light curves of GRS 1915+105 by Maccarone et al (2011) who pointed out the noise relevance in the process responsible of LFQPOs. The possibility of noise-induced quasiperiodic oscillation in the original HR model including three ODEs was also considered by Ryashko & Slepukhina (2017), confirming thus the relevance of the random fluctuations although in different conditions. Turbulence in accretion discs is important because it can provide a driving mechanism also for HFQPOs and can produce the 3:2 twin peak feature, as demonstrated by the numerical model recently developed by Ortega-Rodríguez et al (2020).…”

Section: Resultsmentioning

confidence: 66%

A non-linear mathematical model for the X-ray variability of the microquasar GRS 1915+105 – III. Low-frequency quasi-periodic oscillations

Massaro

Capitanio

Feroci

et al. 2020

Monthly Notices of the Royal Astronomical Society

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The X-ray emission from the microquasar GRS 1915+105 shows, together with a very complex variability on different time scales, the presence of low-frequency quasi periodic oscillations (LFQPO) at frequencies lower than ∼30 Hz. In this paper, we demonstrate that these oscillations can be consistently and naturally obtained as solutions of a system of two ordinary differential equations that is able to reproduce almost all variability classes of GRS 1915+105. We modified the Hindmarsh-Rose model and obtained a system with two dynamical variables x(t), y(t), where the first one represents the X-ray flux from the source, and an input function J(t), whose mean level J0 and its time evolution is responsible of the variability class. We found that for values of J0 around the boundary between the unstable and the stable interval, where the equilibrium points are of spiral type, one obtain an oscillating behaviour in the model light curve similar to the observed ones with a broad Lorentzian feature in the power density spectrum and, occasionally, with one or two harmonics. Rapid fluctuations of J(t), as those originating from turbulence, stabilize the low-frequency quasi periodic oscillations resulting in a slowly amplitude modulated pattern. To validate the model we compared the results with real RXTE data which resulted remarkably similar to those obtained from the mathematical model. Our results allow us to favour an intrinsic hypothesis on the origin of LFQPOs in accretion discs ultimately related to the same mechanism responsible for the spiking limit cycle.

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Section: Resultsmentioning

confidence: 66%

A non-linear mathematical model for the X-ray variability of the microquasar GRS 1915+105 – III. Low-frequency quasi-periodic oscillations

Massaro

Capitanio

Feroci

et al. 2020

Monthly Notices of the Royal Astronomical Society

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“…Note that in case of the finite scale separation, the counterpart of the center point of the fast flow is a weakly unstable focus of the complete system (4). The structure of the fast flow is organized around the saddle-center bifurcation, which occurs at κ = κ SC = −0.1674.…”

Section: Inverse Stochastic Resonance Due To a Trapping Effectmentioning

confidence: 98%

Two paradigmatic scenarios for inverse stochastic resonance

Bačić

Franović

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Inverse stochastic resonance comprises a nonlinear response of an oscillatory system to noise where the frequency of noise-perturbed oscillations becomes minimal at an intermediate noise level. We demonstrate two generic scenarios for inverse stochastic resonance by considering a paradigmatic model of two adaptively coupled stochastic active rotators whose local dynamics is close to a bifurcation threshold. In the first scenario, shown for the two rotators in the excitable regime, inverse stochastic resonance emerges due to a biased switching between the oscillatory and the quasi-stationary metastable states derived from the attractors of the noiseless system. In the second scenario, illustrated for the rotators in the oscillatory regime, inverse stochastic resonance arises due to a trapping effect associated to a noise-enhanced stability of an unstable fixed point. The details of the mechanisms behind the resonant effect are explained in terms of slow-fast analysis of the corresponding noiseless systems.The effects of noise may generically be classified into two groups: on the one hand, the noise may enhance or suppress certain features of deterministic dynamics by acting on the system states in an inhomogeneous fashion, while on the other hand, it may give rise to novel forms of behavior, associated to crossing of thresholds and separatrices, or to a stability of deterministically unstable states. The constructive role of noise has been evinced in a wide range of real-world applications, from neural networks and chemical reactions to lasers and electronic circuits. The classical examples of stochastic facilitation concern the resonant phenomena, including the stochastic resonance, where the noise of appropriate intensity may induce oscillations in bistable systems that are preferentially locked to a weak periodic forcing, and the coherence resonance, where an intermediate level of noise may trigger coherent oscillations in excitable systems. Recently, a novel form of nonlinear response to noise, called inverse stochastic resonance, has been discovered while studying individual neural oscillators and models of neuronal populations. It has come to light that the noise may reduce the intrinsic spiking frequency of neuronal oscillators, transforming the tonic firing into a bursting-like activity or even quenching the oscillations. Within the present study, we demonstrate two paradigmatic mechanisms of inverse stochastic resonance, one based on biased switching between the metastable states, and the other associated to a noise-enhanced stability of an unstable fixed point. We show that the effect is robust, in a sense that it may emerge in coupled excitable and coupled oscillatory systems, and both in cases of Type I and Type II oscillators. a) Electronic mail: franovic@ipb.ac.rs Noise in excitable or multistable systems may fundamentally change their deterministic dynamics, giving rise to qualitatively novel forms of behavior, associated to crossing of thresholds and separatrices, or stabilization of certain unstab...

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“…A study of these kinetic regimes is based on the theory of bifurcations and analysis of basins of attraction. It is well known that in dynamical models with strong nonlinearity even seemingly small random disturbances can complicate behaviour and cause stochastic transport [17][18][19] with various unexpected noise-induced effects [20][21][22][23][24][25][26][27][28][29]. Here, the phenomena of coherence and anti-coherence resonance attract attention of researchers [30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Variability of complex oscillatory regimes in the stochastic model of cold-flame combustion of a hydrocarbon mixture

Bashkirtseva

Slepukhina

2022

Phil. Trans. R. Soc. A.

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Processes of the cold-flame combustion of a mixture of two hydrocarbons are studied on the base of a three-dimensional nonlinear dynamical model. Bifurcation analysis of the deterministic model reveals mono- and bistability parameter zones with equilibrium and oscillatory attractors. For this model, effects of random disturbances in the bistability parameter zone are studied. We show that random forcing causes transitions between coexisting stable equilibria and limit cycles with the formation of complex stochastic mixed-mode oscillations. Properties of these oscillatory regimes are studied by means of statistics of interspike intervals. A phenomenon of anti-coherence resonance is discussed. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

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Noise-induced torus bursting in the stochastic Hindmarsh-Rose neuron model

Cited by 41 publications

References 37 publications

A non-linear mathematical model for the X-ray variability of the microquasar GRS 1915+105 – III. Low-frequency quasi-periodic oscillations

A non-linear mathematical model for the X-ray variability of the microquasar GRS 1915+105 – III. Low-frequency quasi-periodic oscillations

Two paradigmatic scenarios for inverse stochastic resonance

Variability of complex oscillatory regimes in the stochastic model of cold-flame combustion of a hydrocarbon mixture

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