Dynamical Properties of Firing Patterns in the Huber-Braun Cold Receptor Model in Response to External Current Stimuli

We have studied the role of external current stimuli in a four-dimensional Hodgkin-Huxley-type model of cold receptor in this paper. Firstly, we researched its firing patterns from direct current (DC) and alternating current (AC) stimuli. Under different values of DC stimulus intensity, interspike intervals (ISIs) with period-doubling bifurcation phenomena appeared. Second, research has shown that neurons are extremely sensitive to changes in the frequency and amplitude of the current used to stimulate them. As the stimulus frequency increased, discharge rhythms emerged ranging from burst firing to chaotic firing and spiking firing. Meanwhile, various phase-locking patterns have been studied in this paper, such as p : 1 (p > 1), 1 : q (q > 1), 2 : q (q > 1) and p : q (p, q > 1), etc. Finally, based on the fast-slow dynamics analysis, codimension-two bifurcation analysis of the fast subsystem was performed in the parameter (asr, B)-plane. We mainly investigated cusp bifurcation, fold-Hopf bifurcation, Bogdanov-Takens bifurcation and generalized Hopf bifurcation. These results revealed the effect of external current stimuli on the neuronal discharge rhythm and were instructive for further understanding the dynamical properties and mechanisms of the Huber-Braun model.

[1]  Yanqiu Che,et al.  Spike trains in Hodgkin–Huxley model and ISIs of acupuncture manipulations , 2008 .

[2]  P. Shorten,et al.  A Hodgkin-Huxley model exhibiting bursting oscillations , 2000, Bulletin of mathematical biology.

[3]  Tuckwell Henry C,et al.  Spike trains in a stochastic Hodgkin-Huxley system. , 2005, Bio Systems.

[4]  Ulrike Feudel,et al.  Temperature-dependent stochastic dynamics of the Huber-Braun neuron model. , 2011, Chaos.

[5]  Ying Du,et al.  Using interspike intervals to quantify noise effects on spike trains in temperature encoding neurons , 2010, Cognitive Neurodynamics.

[6]  Frank Moss,et al.  Noisy activation kinetics induces bursting in the Huber-Braun neuron model , 2010 .

[7]  Hans A. Braun,et al.  Conductance versus current noise in a neuronal model for noisy subthreshold oscillations and related spike generation , 2006, Biosyst..

[8]  Ling Hong,et al.  Rate of afferent stimulus dependent synchronization and coding in coupled neurons system , 2004 .

[9]  Bin Deng,et al.  Fire patterns of modified HH neuron under external sinusoidal ELF stimulus , 2009 .

[10]  Eugene M. Izhikevich,et al.  Resonate-and-fire neurons , 2001, Neural Networks.

[11]  Hans A Braun,et al.  On the role of subthreshold currents in the Huber-Braun cold receptor model. , 2010, Chaos.

[12]  Xu Jian-Xue,et al.  Propagation of periodic and chaotic action potential trains along nerve fibers , 1997 .

[13]  Svetlana Postnova,et al.  Propagation effects of current and conductance noise in a model neuron with subthreshold oscillations. , 2008, Mathematical biosciences.

[14]  Omri Harish,et al.  Control of the firing patterns of vibrissa motoneurons by modulatory and phasic synaptic inputs: a modeling study. , 2010, Journal of neurophysiology.

[15]  Yanjun Zeng,et al.  Dynamical properties of firing patterns in ELL pyramidal neuron under external electric field stimulus , 2013, Neurological Sciences.

[16]  Hans A Braun,et al.  Neural Synchronization at Tonic-to-Bursting Transitions , 2007, Journal of biological physics.

[17]  Alexander B. Neiman,et al.  Interactions between slow and fast conductances in the Huber/Braun model of cold-receptor discharges , 2000, Neurocomputing.

[18]  F Moss,et al.  Noise-induced impulse pattern modifications at different dynamical period-one situations in a computer model of temperature encoding. , 2001, Bio Systems.

[19]  Yo Horikawa.  A spike train with a step change in the interspike intervals in the FitzHugh-Nagumo model , 1995 .

[20]  Martin Tobias Huber,et al.  Computer Simulations of Neuronal Signal Transduction: The Role of Nonlinear Dynamics and Noise , 1998 .

[21]  Hans A Braun,et al.  Oscillations, resonances and noise: basis of flexible neuronal pattern generation. , 2003, Bio Systems.