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 ma...
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| Format: | Article |
| Language: | Russian |
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Institute of Computer Science
2017-06-01
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| Series: | Компьютерные исследования и моделирование |
| Subjects: | |
| Online Access: | http://crm.ics.org.ru/uploads/crmissues/crm_2017_3/2017_03_07.pdf |
| _version_ | 1818957393827987456 |
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| author | Lev Borisovich Ryashko Eudokia Sergeevna Slepukhina |
| author_facet | Lev Borisovich Ryashko Eudokia Sergeevna Slepukhina |
| author_sort | Lev Borisovich Ryashko |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T11:09:09Z |
| format | Article |
| id | doaj.art-a77df917d61542c19d6e22870c671dd2 |
| institution | Directory Open Access Journal |
| issn | 2076-7633 2077-6853 |
| language | Russian |
| last_indexed | 2024-12-20T11:09:09Z |
| publishDate | 2017-06-01 |
| publisher | Institute of Computer Science |
| record_format | Article |
| series | Компьютерные исследования и моделирование |
| spelling | doaj.art-a77df917d61542c19d6e22870c671dd22022-12-21T19:42:51ZrusInstitute of Computer ScienceКомпьютерные исследования и моделирование2076-76332077-68532017-06-019344946810.20537/2076-7633-2017-9-3-449-4682586Analysis of additive and parametric noise effects on Morris - Lecar neuron modelLev Borisovich RyashkoEudokia Sergeevna SlepukhinaThis 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.http://crm.ics.org.ru/uploads/crmissues/crm_2017_3/2017_03_07.pdfMorris – Lecar modelneural excitabilityGaussian noisenoise-induced transitionsstochastic sensitivityconfidence domains |
| spellingShingle | Lev Borisovich Ryashko Eudokia Sergeevna Slepukhina Analysis of additive and parametric noise effects on Morris - Lecar neuron model Компьютерные исследования и моделирование Morris – Lecar model neural excitability Gaussian noise noise-induced transitions stochastic sensitivity confidence domains |
| title | Analysis of additive and parametric noise effects on Morris - Lecar neuron model |
| title_full | Analysis of additive and parametric noise effects on Morris - Lecar neuron model |
| title_fullStr | Analysis of additive and parametric noise effects on Morris - Lecar neuron model |
| title_full_unstemmed | Analysis of additive and parametric noise effects on Morris - Lecar neuron model |
| title_short | Analysis of additive and parametric noise effects on Morris - Lecar neuron model |
| title_sort | analysis of additive and parametric noise effects on morris lecar neuron model |
| topic | Morris – Lecar model neural excitability Gaussian noise noise-induced transitions stochastic sensitivity confidence domains |
| url | http://crm.ics.org.ru/uploads/crmissues/crm_2017_3/2017_03_07.pdf |
| work_keys_str_mv | AT levborisovichryashko analysisofadditiveandparametricnoiseeffectsonmorrislecarneuronmodel AT eudokiasergeevnaslepukhina analysisofadditiveandparametricnoiseeffectsonmorrislecarneuronmodel |