Nonlinear dynamics of direction-selective recurrent neural media

Area of Science:

• Computational Neuroscience
• Systems Neuroscience
• Mathematical Biology

Background:

• Direction selectivity in cortical neurons is crucial for sensory processing.
• Asymmetric lateral connections are a proposed mechanism for neural direction selectivity.
• Previous studies often simplified network dynamics by neglecting nonlinearities.

Purpose of the Study:

• To mathematically analyze neural network dynamics with asymmetric lateral connections, incorporating nonlinearities.
• To investigate the emergence of stimulus-locked traveling pulse solutions.
• To explore the stability breakdown of these solutions and the resulting activity patterns.

Main Methods:

• Mathematical analysis of a class of direction-selective neural models.
• Inclusion of nonlinear dynamics, contrasting with prior linear systems approaches.
• Analysis of traveling pulse solutions and their stability bifurcations.

Main Results:

• Asymmetrically coupled networks can stabilize stimulus-locked traveling pulse solutions.
• These solutions are suitable for modeling direction-selective neuronal responses.
• Instability arises outside specific stimulus speed regimes, generating 'lurching' activity waves with distinct spatiotemporal periodicity.

Conclusions:

• Nonlinear dynamics in asymmetrically connected neural networks can generate robust direction selectivity.
• The identified 'lurching' activity waves and their bifurcations offer novel insights beyond classical models.
• This work provides a framework for distinguishing between different mechanisms of direction selectivity in neurophysiological experiments.