Delay, noise and phase locking in pulse coupled neural networks.

Area of Science:

• Computational Neuroscience
• Network Dynamics
• Nonlinear Systems

Background:

• Phase-locked states are crucial for neural synchrony.
• Understanding the impact of delays and noise on neural networks is essential for modeling brain function.
• Existing models often simplify network connectivity and delay dynamics.

Purpose of the Study:

• To investigate the influence of varying delay times and noise on the stability of phase-locked states.
• To analyze these effects in both the lighthouse and integrate-and-fire neural network models.
• To characterize the emergent dynamics, such as relaxation oscillations, under these conditions.

Main Methods:

• Simulations of pulse-coupled neural networks using the lighthouse and integrate-and-fire models.
• Systematic variation of delay times and noise levels in the coupling.
• Analysis of network stability and emergent oscillatory behaviors.

Main Results:

• Increased delay times consistently weaken the stability of the phase-locked state in both models.
• Noise exacerbates the destabilizing effect of delays.
• Relaxation oscillations emerge as a common dynamical regime with increasing delay times.

Conclusions:

• Delay times are a critical factor in maintaining neural synchrony and network stability.
• Arbitrary coupling delays can lead to complex dynamics like relaxation oscillations.
• The findings provide insights into the robustness and limitations of neural synchronization mechanisms.