Transition to bursting via deterministic chaos.

Area of Science:

• Computational Neuroscience
• Nonlinear Dynamics
• Statistical Physics

Background:

• Neuronal models exhibit diverse firing patterns, including regular spiking and bursting.
• Transitions between firing modes are critical for understanding neural dynamics.
• Irregular dynamics, such as chaos, can precede or accompany complex behaviors like bursting.

Purpose of the Study:

• To investigate the statistical properties of irregular bursting in neuronal models near the spiking-to-bursting transition.
• To characterize the influence of chaotic attractors on burst dynamics.
• To analyze how burst statistics change with proximity to the critical transition.

Main Methods:

• Analysis of a class of neuronal models exhibiting a transition from spiking to bursting.
• Identification and characterization of chaotic attractors preceding the bursting regime.
• Statistical analysis of burst duration, number of spikes per burst, and interspike interval distributions.

Main Results:

• Chaotic attractors emerge prior to the bursting transition, generating irregular spiking.
• This irregular spiking underlies the observed irregular bursting dynamics.
• Burst durations can become significantly prolonged near the critical transition.
• The study quantifies the statistics of spike counts and interspike intervals within bursts as a function of distance from criticality.

Conclusions:

• Irregular bursting in these models is a consequence of underlying chaotic dynamics.
• The transition region offers a unique regime for studying complex neural dynamics.
• Understanding these statistical properties provides insights into neural computation and information processing in critical regimes.