High-order synchronization in identical neurons with asymmetric pulse coupling

Area of Science:

• Computational Neuroscience
• Nonlinear Dynamics
• Systems Biology

Background:

• High-order (p/q) synchronization, where p cycles of one oscillator match q cycles of another, is known in forced and coupled oscillators.
• This phenomenon is less understood in coupled neuronal systems, particularly concerning asymmetric coupling effects.

Purpose of the Study:

• To demonstrate and thoroughly investigate high-order (p/q) frequency-locking in a pair of coupled neurons with identical intrinsic frequencies but asymmetric coupling.
• To analyze the complex structure and dynamics within these synchronization regions in parameter space.

Main Methods:

• Simulations were used to explore the parameter space (g,α) and observe phenomena like quasiperiodicity, devil staircase, and Farey arrangements of spike sequences.
• An analytical method based on event-driven maps was developed to determine the existence and stability of p/q frequency-locked states, handling nonsmooth bifurcations.

Main Results:

• Asymmetric coupling in an excitatory-inhibitory (E-I) neuron pair naturally induces diverse p/q frequency-locking structures.
• Simulations revealed reducible and irreducible p/q regions with internal bifurcation structures, unlike traditional Arnold tongues.
• Multistability was observed both within and between different p/q synchronization states, with boundaries defined by saddle node and grazing bifurcations.

Conclusions:

• Asymmetric coupling is a key mechanism for generating complex synchronization patterns in neuronal networks.
• The developed analytical method provides a robust framework for understanding spike sequence stability in coupled neuron models.
• The findings highlight the intricate dynamics and multistability inherent in neuronal synchronization, crucial for understanding neural computation.