Huber-Braun neuron dynamics

We study a physiologically realistic implementation of internal stochasticity in a four dimensional Hodgkin-Huxley (HH) type model of cold receptors. We show that in a deterministically tonic-firing regime, changing the parameters can drive the neuron into a state of complex bursting behavior. An explanation of the mechanism behind this effect is given in terms of a bifurcation diagram of inter-spike interval (ISI) as the temperature and external current are altered.

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Measuring effects of different noises in a model using ISI-distance methods

International Journal of Biomathematics ◽

10.1142/s1793524515500436 ◽

2015 ◽

Vol 08 (04) ◽

pp. 1550043

Author(s):

Jingyi Qu ◽

Rubin Wang ◽

Ying Du

Keyword(s):

Interspike Interval ◽

Type Model ◽

Firing Regime ◽

Interspike Intervals ◽

Tonic Firing ◽

Interval Method ◽

Firing Rates ◽

Complementary Approach ◽

Distance Methods ◽

Chaotic Burst

This paper examines the effects of current and conductance noises in a minimal Hodgkin–Huxley type model of a cold receptor neuron. Current noise enters the membrane equation directly while conductance noise is propagated through the activation variables. Compared with common used interspike interval method, ISI-distance is a simple complementary approach to measure the different effects of current and conductance noises. ISI-distance extracts information from the interspike intervals by evaluating the ratio of instantaneous firing rates, which is parameter-free, time scale-independent and easy to visualize. Simulation results show that the most significant differences between different noise implementations in a pacemaker-like tonic firing regime at the transition to chaotic burst discharges.

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On the chaotic pole of attraction for Hindmarsh-Rose neuron dynamics with external current input

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.5083180 ◽

2019 ◽

Vol 29 (2) ◽

pp. 023104 ◽

Cited By ~ 5

Author(s):

Emile Franck Doungmo Goufo ◽

Conrad Bertrand Tabi

Keyword(s):

External Current ◽

Current Input ◽

Neuron Dynamics

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VEGETATION PATTERN FORMATION IN A SEMI-ARID CLIMATE

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127411030696 ◽

2011 ◽

Vol 21 (12) ◽

pp. 3497-3509 ◽

Cited By ~ 14

Author(s):

HENK A. DIJKSTRA

Keyword(s):

Bifurcation Diagram ◽

Selection Process ◽

Vegetation Pattern ◽

Numerical Continuation ◽

Arid Climate ◽

Type Model ◽

Vegetation Patterns ◽

Diffusion Type ◽

Positive Feedbacks ◽

Semi Arid

A partial bifurcation diagram of a reaction–diffusion type model of two-dimensional vegetation patterns in a semi-arid climate is computed using numerical continuation techniques. In previous studies with this model, it has been shown that two positive feedbacks (the infiltration feedback and precipitation feedback) may influence the type of vegetation patterns which appear under a certain precipitation forcing. In this bifurcation study, first the case is considered where the infiltration feedback is the only positive feedback. The partial bifurcation diagram of the different steady states is more complicated than earlier model results have suggested and provides insight into how the pattern selection process takes place. Finally, it is shown that when the precipitation feedback is included, the bifurcation diagram is only shifted to smaller precipitation values.

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