Bifurcation analysis of a Morris–Lecar neuron model

Liu, Congmin; Liu, Xuanliang; Liu, Shenquan

doi:10.1007/s00422-013-0580-4

Cited by 50 publications

(31 citation statements)

References 11 publications

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“…For BHom, ∂ I /∂ V > 0, which corresponds to the net perithreshold current at steady-state being inward. Investigations for the SNIC and SubH can can be found in the literature 21 , while the I–V curves for saddle-node bifurcations, SupH, and BHom are new findings. ∂ I /∂ V = 0, ∂ I /∂ V < 0, and ∂ I /∂ V > 0 were proved as the necessary conditions for SNIC and SN bifurcations, SubH and SupH bifurcations, and for BHom bifurcations, respectively.…”

Section: Resultsmentioning

confidence: 82%

“…For example, class I excitability corresponds to a resting state (stable equilibrium) changed to firing (limit cycle) via saddle-node on invariant circle (SNIC) bifurcation as the depolarization current increases; meanwhile, class II excitability corresponds to Andronov-Hopf bifurcations 1–3 , which have been widely investigated in the classical 2-dimensional Morris-Lecar (ML) model with variables ( V , w ) 3, 16, 19–21 . The position relationship between 2 nullclines is different for the 2 classes of excitability.…”

Section: Introductionmentioning

confidence: 99%

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Transitions between classes of neuronal excitability and bifurcations induced by autapse

Zhao

2017

Sci Rep

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Neuronal excitabilities behave as the basic and important dynamics related to the transitions between firing and resting states, and are characterized by distinct bifurcation types and spiking frequency responses. Switches between class I and II excitabilities induced by modulations outside the neuron (for example, modulation to M-type potassium current) have been one of the most concerning issues in both electrophysiology and nonlinear dynamics. In the present paper, we identified switches between 2 classes of excitability and firing frequency responses when an autapse, which widely exists in real nervous systems and plays important roles via self-feedback, is introduced into the Morris-Lecar (ML) model neuron. The transition from class I to class II excitability and from class II to class I spiking frequency responses were respectively induced by the inhibitory and excitatory autapse, which are characterized by changes of bifurcations, frequency responses, steady-state current-potential curves, and nullclines. Furthermore, we identified codimension-1 and -2 bifurcations and the characteristics of the current-potential curve that determine the transitions. Our results presented a comprehensive relationship between 2 classes of neuronal excitability/spiking characterized by different types of bifurcations, along with a novel possible function of autapse or self-feedback control on modulating neuronal excitability.

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Section: Resultsmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Transitions between classes of neuronal excitability and bifurcations induced by autapse

Zhao

2017

Sci Rep

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“…The Morris-Lecar model is known to generate different dynamical regimes depending on its parameters 19,20 . We fixed the values of β w = −10 mV and γ w = 13 mV and used two values of β m to obtain the two classes of excitability.…”

Section: A Morris-lecar Modelmentioning

confidence: 99%

Characterizing signal encoding and transmission in class I and class II neurons via ordinal time-series analysis

Estarellas

Masoliver

Masoller

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Neurons encode and transmit information in spike sequences. However, despite the effort devoted to quantify their information content, little progress has been made in this regard. Here we use a nonlinear method of time-series analysis (known as ordinal analysis) to compare the statistics of spike sequences generated by applying an input signal to the neuronal model of Morris-Lecar. In particular we consider two different regimes for the neurons which lead to two classes of excitability: class I, where the frequency-current curve is continuous and class II, where the frequency-current curve is discontinuous. By applying ordinal analysis to sequences of inter-spike-intervals (ISIs) our goals are (1) to investigate if different neuron types can generate spike sequences which have similar symbolic properties; (2) to get deeper understanding on the effects that electrical (diffusive) and excitatory chemical (i.e., excitatory synapse) couplings have; and (3) to compare, when a small-amplitude periodic signal is applied to one of the neurons, how the signal features (amplitude and frequency) are encoded and transmitted in the generated ISI sequences for both class I and class II type neurons and electrical or chemical couplings. We find that depending on the frequency, specific combinations of neuron/class and coupling-type allow a more effective encoding, or a more effective transmission of the signal. a) ElectronicSensory neurons detect, encode and transmit information of external temporal stimuli (input signals such as visual, auditory, olfactory, etc.) in sequences of spikes, also known as action potentials. Despite decades of effort to understand how information is processed, the underlying mechanisms of neuronal encoding are still not fully understood. Different coding mechanisms have been proposed in the literature, which can be more or less effective depending on the level of environmental noise, the level of the external signal, and its frequency. Here we focus on the encoding of a small-amplitude periodic signal. We use a well-known neuron model to investigate the role of the excitability class of the neurons (either class I or class II) and of the type of coupling (electrical or chemical) to a second neuron that does not perceive the external signal. We find that the neuron can encode the signal in the form of preferred (more expressed) temporal spike patterns, regardless of the class of neuron and of the type of coupling. On the contrary, depending on the signal frequency, specific combinations of neuron-class and coupling-type allow a more effective encoding, or a more effective transmission of the signal.

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“…Детальный бифуркационный анализ детерминированной модели МЛ в различных параметрических зонах представлен, например, в работах [22,30]. Стохастический вариант модели исследовался в [9,10,16,17,24,26,29].…”

Section: е с слепухинаunclassified

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

Slepukhina¹

2016

Nelin. Dinam.

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Bifurcation analysis of a Morris–Lecar neuron model

Cited by 50 publications

References 11 publications

Transitions between classes of neuronal excitability and bifurcations induced by autapse

Transitions between classes of neuronal excitability and bifurcations induced by autapse

Characterizing signal encoding and transmission in class I and class II neurons via ordinal time-series analysis

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

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