Network-induced chaos in integrate-and-fire neuronal ensembles

Area of Science:

• Computational neuroscience
• Dynamical systems theory
• Computational physics

Background:

• Single linear integrate-and-fire (IF) neurons typically do not exhibit chaotic dynamics.
• The role of network interactions in inducing chaos in neuronal models remains an active area of research.

Purpose of the Study:

• To investigate whether conductance-based, pulse-coupled network interactions can induce chaotic dynamics in an IF neuronal ensemble.
• To characterize the largest Lyapunov exponent in these high-dimensional, nonsmooth dynamical systems.
• To develop a stable and accurate numerical algorithm for evaluating the largest Lyapunov exponent.

Main Methods:

• Numerical simulations of all-to-all, homogeneously pulse-coupled IF neuronal networks.
• Analysis of dynamical systems under external periodic current drive.
• Development and application of a novel numerical algorithm for Lyapunov exponent calculation.

Main Results:

• All-to-all, homogeneously pulse-coupled IF neuronal networks can exhibit chaotic dynamics when subjected to an external periodic current drive.
• A precise characterization of the largest Lyapunov exponent for these complex systems was achieved.
• A stable and accurate numerical algorithm was presented, overcoming limitations of traditional methods for nonsmooth systems.

Conclusions:

• Neuronal network interactions, specifically homogeneous pulse-coupling in IF networks, are capable of inducing chaotic dynamics.
• The developed numerical method offers a robust approach for analyzing chaos in complex, nonsmooth neuronal systems.
• This research advances our understanding of complex dynamics in neuronal ensembles.