Analysis of additive and parametric noise effects on Morris - Lecar neuron model

This paper is devoted to the analysis of the effect of additive and parametric noise on the processes occurring in the nerve cell. This study is carried out on the example of the well-known Morris - Lecar model described by the two-dimensional system of ordinary differential equations. One of the main properties of the neuron is the excitability, i.e., the ability to respond to external stimuli with an abrupt change of the electric potential on the cell membrane. This article considers a set of parameters, wherein the model exhibits the class 2 excitability. The dynamics of the system is studied under variation of the external current parameter. We consider two parametric zones: the monostability zone, where a stable equilibrium is the only attractor of the deterministic system, and the bistability zone, characterized by the coexistence of a stable equilibrium and a limit cycle. We show that in both cases random disturbances result in the phenomenon of the stochastic generation of mixed-mode oscillations (i. e., alternating oscillations of small and large amplitudes). In the monostability zone this phenomenon is associated with a high excitability of the system, while in the bistability zone, it occurs due to noise-induced transitions between attractors. This phenomenon is confirmed by changes of probability density functions for distribution of random trajectories, power spectral densities and interspike intervals statistics. The action of additive and parametric noise is compared. We show that under the parametric noise, the stochastic generation of mixed-mode oscillations is observed at lower intensities than under the additive noise. For the quantitative analysis of these stochastic phenomena we propose and apply an approach based on the stochastic sensitivity function technique and the method of confidence domains. In the case of a stable equilibrium, this confidence domain is an ellipse. For the stable limit cycle, this domain is a confidence band. The study of the mutual location of confidence bands and the boundary separating the basins of attraction for different noise intensities allows us to predict the emergence of noise-induced transitions. The effectiveness of this analytical approach is confirmed by the good agreement of theoretical estimations with results of direct numerical simulations. © 2017 Lev B. Ryashko, Evdokia S. Slepukhina.The work was supported by the Government of the Russian Federation (Act 211, contract No. Russian Foundation for Basic Research (project No. 16-31-00317 mol_a)

Stochastic Bifurcations and Noise-Induced Chaos in 3D Neuron Model

The stochastically forced three-dimensional Hindmarsh-Rose model of neural activity is considered. We study the effect of random disturbances in parametric zones where the deterministic model exhibits mono- and bistable dynamic regimes with period-adding bifurcations of oscillatory modes. It is shown that in both cases the phenomenon of noise-induced bursting is observed. In the monostable zone, where the only attractor of the system is a stable equilibrium, this effect is connected with a stochastic generation of large-amplitude oscillations due to the high excitability of the model. In a parametric zone of coexisting stable equilibria and limit cycles, bursts appear due to noise-induced transitions between the attractors. For a quantitative analysis of the noise-induced bursting and corresponding stochastic bifurcations, an approach based on the stochastic sensitivity function (SSF) technique is applied. Our estimations of the strength of noise that generates such qualitative changes in stochastic dynamics are in a good agreement with the direct numerical simulation. A relationship of the noise-induced generation of bursts with transitions from order to chaos is discussed. © 2016 World Scientific Publishing Company

Stochastic Generation of Large-Amplitude Oscillations in a Three-Dimensional Model of Cold-Flame Combustion of a Hydrocarbon Mixture

We study a stochastic 3D model of cold-flame combustion of a hydrocarbon mixture. We show that noise can induce large-amplitude oscillations from the equilibrium regime. We analyze this phenomenon by means of the stochastic sensitivity function technique and the method of confidence domains.Исследование выполнено за счет гранта РФФИ (проект № 20-01-00165)

STOCHASTIC OSCILLATIONS NEAR THE “BLUE SKY CATASTROPHE” BIFURCATION IN NEURON MODEL

We study the stochastic Hindmarsh-Rose neuron model near the “blue sky catastrophe” bifurcation. This specific bifurcation describes a particular type of transition between tonic spiking and bursting oscillations in the considered model. We show that noise can induce the changes of frequency and amplitude characteristics of bursting oscillations in this model. Moreover, in the parameter zone of tonic spiking regime, the increase of the noise intensity can lead to the stochastic generation of bursting oscillations. We perform the analysis of these phenomena on the base of the stochastic sensitivity functions technique and the confidence domains method.Исследование выполнено за счет гранта Российского научного фонда (проект № 16-11-10098)

NOISE-INDUCED QUASI-PERIODIC OSCILLATIONS IN HINDMARSH-ROSE NEURON MODEL

We study the phenomenon of noise-induced quasi-periodic oscillations in the stochastic Hindmarsh-Rose neuron model. We show that with the increase of the noise intensity the periodic regime in this model transforms into the quasi-periodic one with the formation of the stochastic torus. We perform the analysis of this phenomenon on the base of the stochastic sensitivity functions technique and the confidence domains method

STOCHASTIC GENERATION OF EARLY AFTERDEPOLARIZATIONS IN A THREE-DIMENSIONAL MODEL OF CARDIAC ACTION POTENTIAL IN A QUIESCENT MODE

We study a stochastic three-dimensional model of cardiac action potential. We show that noise can induce pathological early afterdepolarizations in a quiescent mode. We analyze this phenomenon by means of statistics of interspike intervals and the stochastic sensitivity functions method

Трудности лечения осложнений и реабилитации после COVID-19. Клинический случай

The severe course of the new coronavirus infection (COVID-19) is associated with multiple life-threatening complications that lead to delayed initiation of active rehabilitation and unfavorable long-term treatment outcomes. Tracheoesophageal fistula is one of these complications. The specific feature of this event in COVID-19 is delayed tissue regeneration which requires a non-standard approach to management of such patients.The article presents a clinical case of a pregnant patient after a complicated severe course of COVID-19 with the development of tracheoesophageal fistula, sepsis, and weakness syndrome acquired in ICU. The combination of complications of the disease led to a prolonged (about five months) period of rehabilitation.Modern standard components of intensive therapy of such patients including regular monitoring of endotracheal/tracheostomy tube cuff pressure, dynamic assessment of nutritional status and its correction, rational antimicrobial therapy, screening of psychiatric disorders and early rehabilitation, will minimize the number of both early and delayed complications of COVID-19.  Тяжелое течение новой коронавирусной инфекции (COVID-19) сопряжено со множеством жизнеугрожающих осложнений, которые приводят к отсрочке начала активных реабилитационных мероприятий и ухудшению долгосрочных результатов лечения. Одним из таких осложнений является формирование трахеопищеводного свища. Особенностью этой патологии при COVID-19 является замедленная регенерация тканей, что требует нестандартного подхода к тактике ведения таких пациентов.В статье представлен клинический случай лечения беременной пациентки после осложненного тяжелого течения COVID-19 с развитием трахеопищеводного свища, сепсиса, синдрома приобретенной в отделении реанимации и интенсивной терапии слабости. Комбинация осложнений заболевания привела к затяжному (около 5 мес.) периоду реабилитации.Современные стандартные компоненты интенсивной терапии таких пациентов, включая регулярный контроль давления в манжете эндотрахеальных/трахеостомических трубок, динамическую оценку нутритивного статуса и его коррекцию, рациональную антимикробную терапию, скрининг психических нарушений и раннюю реабилитацию, позволят минимизировать число как ранних, так и отсроченных осложнений COVID-19

Noise-induced large amplitude oscillations in the Morris - Lecar neuron model with class 1 excitability

We consider the Morris - Lecar neuron model with a parameter set corresponding to class 1 excitability. We study the effect of random disturbances on the model in the parametric zone where the only attractor of the deterministic system is a stable equilibrium. We show that under noise the stochastic generation of large amplitude oscillations occurs in the system. This phenomenon is confirmed by changes in distributions of random trajectories and interspike intervals. This effect is analyzed using the stochastic sensitivity function technique and the method of confidence domains. We suggest a criterion for the estimation of threshold values of noise intensity leading to the stochastic generation of oscillations

Stochastic Bifurcations and Noise-Induced Chaos in 3D Neuron Model

The stochastically forced three-dimensional Hindmarsh–Rose model of neural activity is considered. We study the effect of random disturbances in parametric zones where the deterministic model exhibits mono- and bistable dynamic regimes with period-adding bifurcations of oscillatory modes. It is shown that in both cases the phenomenon of noise-induced bursting is observed. In the monostable zone, where the only attractor of the system is a stable equilibrium, this effect is connected with a stochastic generation of large-amplitude oscillations due to the high excitability of the model. In a parametric zone of coexisting stable equilibria and limit cycles, bursts appear due to noise-induced transitions between the attractors. For a quantitative analysis of the noise-induced bursting and corresponding stochastic bifurcations, an approach based on the stochastic sensitivity function (SSF) technique is applied. Our estimations of the strength of noise that generates such qualitative changes in stochastic dynamics are in a good agreement with the direct numerical simulation. A relationship of the noise-induced generation of bursts with transitions from order to chaos is discussed.<br/