Bifurcations and excitability in the temperature-sensitive Morris–Lecar neuron

Xing, Miaomiao; Song, Xiaoqiu; Yang, Zhuoqin; Chen, Yong

doi:10.1007/s11071-020-05667-7

Cited by 33 publications

(13 citation statements)

References 38 publications

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“…Multiple researchers have studied various factors that influence the firing activities in neurons and other excitable cells [9], [10], [11], [12]. The effect of direct current stimulus [14], temperature [15], pressure [16], time-delay [17] and environmental noise [18] have been investigated. Magnetic induction is another factor that affects the neuron membrane potential significantly, which has been observed in physiological experiments [19], [20].…”

Section: Introductionmentioning

confidence: 99%

Numerical bifurcation analysis of improved denatured Morris-Lecar neuron model

Fatoyinbo¹,

Muni²,

Ghosh³

et al. 2022

Preprint

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It is well-known that the electrical activities of neurons are induced by a wide variety of external factors. This work considers the effect of electromagnetic induction on improved denatured Morris-Lecar neuron model. The dependence of dynamical behaviour of the original denatured Morris-Lecar model on parameters is addressed through numerical bifurcation analysis. This allows us to explore the changes in dynamics of the model qualitatively as parameters are varied. Then we investigate the effects of external periodic current and electromagnetic flux on the dynamical properties of the improved denatured Morris-Lecar neuron model. Different types of dynamical behaviour, ranging from regular periodic spiking to complex bursting, are found when the multiple parameters are varied simultaneously. The improved model could be applied to research where simple models are required for physiological and pathophysiological responses in neurons.

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Section: Introductionmentioning

confidence: 99%

Numerical bifurcation analysis of improved denatured Morris-Lecar neuron model

Fatoyinbo¹,

Muni²,

Ghosh³

et al. 2022

Preprint

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“…Due to both types of excitability are very important, the dynamics or bifurcations related to type I excitability and type II excitability, and the dynamics or bifurcations for the transition between excitability types have attracted much attention in both theoretical studies [59][60][61][62][63][64][65] and biological experiments [27][28][29][30][31][32][33][34][35][36][37]. In the biological experiments, the switch between type I excitability and type II excitability was identified and induced by multiple modulations such as the M-type potassium current, A-type current, optogenetic stimulation, and in vitro or in vivo-like conditions, and so on [28-30, 35, 57, 58, 64].…”

Section: Introductionmentioning

confidence: 99%

Multiple and Complex Codimension-2 Bifurcations underlying Post-inhibitory Rebound Spike and Excitability Transition

Wang

et al. 2021

Preprint

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Neuron exhibits nonlinear dynamics such as excitability transition and post-inhibitory rebound (PIR) spike related to bifurcations, which are associated with information processing, locomotor modulation, or brain disease. PIR spike is evoked by inhibitory stimulation instead of excitatory stimulation, which presents a challenge to the threshold concept. In the present paper, 7 codimension-2 or degenerate bifurcations related to 10 codimension-1 bifurcations are acquired in a neuronal model, which presents the bifurcations underlying the excitability transition and PIR spike. Type I excitability corresponds to saddle-node bifurcation on an invariant cycle (SNIC) bifurcation, and type II excitability to saddle-node (SN) bifurcation or sub-critical Hopf (SubH) bifurcation or sup-critical Hopf (SupH) bifurcation. The excitability transition from type I to II corresponds to the codimension-2 bifurcation, Saddle-Node Homoclinic orbit (SNHO) bifurcation, via which SNIC bifurcation terminates and meanwhile big homoclinic orbit (BHom) bifurcation and SN bifurcation emerge. A degenerate bifurcation via which BHom bifurcation terminates and fold limit cycle (LPC) bifurcation emerges is responsible for spiking transition from type I to II, and the roles of other codimension-2 bifurcations (Cusp, Bogdanov-Takens, and Bautin) are discussed. In addition, different from the widely accepted viewpoint that PIR spike is mainly evoked near Hopf bifurcation rather than SNIC bifurcation, PIR spike is identified to be induced near SNIC or BHom or LPC bifurcations, and threshold curves resemble that of Hopf bifurcation. The complex bifurcations present comprehensive and deep understandings of excitability transition and PIR spike, which are helpful for the modulation to neural firing activities and physiological functions.

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“…These neuron models have demonstrated different electrical activities and attracted many researchers' attention. For example, the FHN neuron model exhibits discontinuous transition between different oscillations [ 7 ] and double coherence resonance induced by phase noise [ 8 ]; the HH neuron model displays evoking spiking caused by enough noise intensity [ 9 ], chaotic resonance dependent on current intensity [ 10 ], and extrinsic stochastic resonance caused by ion shot noise [ 11 ]; in the presence of periodic input, the HR neuron model can show nonlinear resonance behavior [ 12 ], periodic and chaotic firing patterns [ 13 ], transition between chaotic firing and periodic firing [ 14 ], and bursting phenomenon [ 15 ]; the Izhikevich neuron model can appear chaotic resonance [ 16 , 17 ]; the ML neuron model can exhibit mono- and bistable dynamic regimes [ 18 ] and responses to two temperature-sensitive ion channels, calcium and leak current, respectively [ 19 ]. These classical models and their dynamical analysis are motivating researchers to develop more realistic or refined neuron models.…”

Section: Introductionmentioning

confidence: 99%

Multiple Firing Patterns in Coupled Hindmarsh-Rose Neurons with a Nonsmooth Memristor

Shi

Wang

2020

Neural Plasticity

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A model is introduced by coupling two three-dimensional Hindmarsh-Rose models with the help of a nonsmooth memristor. The firing patterns dependent on the external forcing current are explored, which undergo a process from adding-period to chaos. The stability of equilibrium points of the considered model is investigated via qualitative analysis, from which it can be gained that the model has diversity in the number and stability of equilibrium points for different coupling coefficients. The coexistence of multiple firing patterns relative to initial values is revealed, which means that the referred model can appear various firing patterns with the change of the initial value. Multiple firing patterns of the addressed neuron model induced by different scales are uncovered, which suggests that the discussed model has a multiscale effect for the nonzero initial value.

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Bifurcations and excitability in the temperature-sensitive Morris–Lecar neuron

Cited by 33 publications

References 38 publications

Numerical bifurcation analysis of improved denatured Morris-Lecar neuron model

Numerical bifurcation analysis of improved denatured Morris-Lecar neuron model

Multiple and Complex Codimension-2 Bifurcations underlying Post-inhibitory Rebound Spike and Excitability Transition

Multiple Firing Patterns in Coupled Hindmarsh-Rose Neurons with a Nonsmooth Memristor

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