Widespread neuronal chaos induced by slow oscillating currents.

Area of Science:

• Computational Neuroscience
• Dynamical Systems Theory
• Mathematical Biology

Background:

• Understanding the origins of chaotic dynamics in individual neuron models is crucial for comprehending complex brain functions.
• Previous models often simplify the intricate interplay of intrinsic currents and their impact on neural excitability.

Purpose of the Study:

• To investigate the genesis and onset of chaos in a mathematical model of a single neuron.
• To elucidate the role of fast-slow dynamics and codimension-2 bifurcations in organizing neural activity regimes.

Main Methods:

• Analysis of 3D fast and 2D slow dynamics governing intrinsic neuronal currents.
• Identification of homoclinic connections, saddle equilibria, and periodic orbit bifurcations.
• Application of parameter continuation, symbolic techniques, and Lyapunov exponents for bifurcation analysis.

Main Results:

• Discovered multiple codimension-2 bifurcations (Shilnikov-Hopf, Belyakov, Bautin, Bogdanov-Takens) organizing the parameter space.
• Identified routes to chaos at the intersections of quiescent, tonic spiking, and bursting activity regimes.
• Reduced the high-dimensional model to a 1D return map, effectively capturing complex dynamics.

Conclusions:

• The fast-slow dynamics are central to the emergence of chaos and complex activity patterns in this neural model.
• The identified bifurcations provide a framework for understanding the transition between different firing modes.
• The reduced 1D map offers a powerful tool for analyzing and explaining intricate neural dynamics.