Self-exciting chaos as a dynamic model for irregular neural spiking

Area of Science:

• Neuroscience
• Dynamical Systems Theory
• Computational Neuroscience

Background:

• Neurons exhibit complex, irregular firing patterns.
• Understanding the mechanisms behind neuronal spike sequences is crucial for neuroscience.
• Temporal coding in neural systems remains an active area of research.

Purpose of the Study:

• Introduce a novel nonlinear dynamical system with self-exciting chaotic dynamics.
• Investigate the synchronization of spike sequences under noisy perturbations.
• Explore the potential of self-exciting chaos for temporal coding in neural systems.

Main Methods:

• Development of a nonlinear dynamical system model.
• Analysis of interspike interval return maps.
• Simulation of spike sequences from various initial conditions.
• Introduction of noisy perturbations to observe synchronization phenomena.

Main Results:

• The system demonstrates self-exciting chaotic dynamics.
• Interspike interval return maps show a noisy Poisson-like distribution.
• Spike sequences from different initial conditions are initially unrelated but synchronize with noisy perturbations.
• The model's features align with experimental data on irregular neuronal firing.

Conclusions:

• Self-exciting chaos provides a viable mechanism for generating irregular spike sequences in neurons.
• Noisy perturbations can induce synchronization in chaotic neural dynamics.
• This model offers a potential framework for understanding temporal coding of complex input signals in the brain.