A discrete Huber-Braun neuron model: from nodal properties to network performance

Area of Science:

• Computational Neuroscience
• Mathematical Biology
• Complex Systems

Background:

• Traditional neuron models are continuous and complex.
• Discrete models offer simplified yet effective replication of neuronal dynamics.
• Understanding neuronal network behavior is crucial for neuroscience.

Purpose of the Study:

• To introduce a novel discrete neuron model based on the Huber-Braun model.
• To investigate the impact of temperature-dependent ion channels on neuronal firing patterns.
• To analyze the spatiotemporal dynamics and wave propagation in single- and two-layer networks with obstacles.

Main Methods:

• Derivation of a discrete neuron model incorporating slow and subthreshold currents.
• Analysis of chaotic and periodic regions using bifurcation and Lyapunov exponents.
• Application of sample entropy to quantify model complexity.
• Simulation of single- and two-layer networks with obstacles and varying stimuli.
• Investigation of spiral wave formation and propagation dynamics.

Main Results:

• The discrete model successfully replicates complex neuronal dynamics.
• Temperature variations influence the neuron's firing patterns.
• Obstacles disrupt wave propagation, inducing re-entry and spiral waves in networks.
• Two-layer network behavior is significantly affected by obstacle placement and stimulus application.

Conclusions:

• The proposed discrete neuron model provides a computationally efficient approach to studying neuronal dynamics.
• Temperature-dependent ion channels add a layer of complexity to neuronal firing.
• Network architecture and external factors like obstacles and stimuli critically shape spatiotemporal patterns.
• This model offers insights into phenomena like coherence resonance and wave re-entry in neural systems.