Deterministic excitable media under Poisson drive: power law responses, spiral waves, and dynamic range

Area of Science:

• Complex systems
• Nonlinear dynamics
• Computational neuroscience

Background:

• Excitable media exhibit wave phenomena crucial for information processing.
• Network activity in excitable media is influenced by external stimuli and internal dynamics.
• Understanding the response function is key to deciphering neural coding.

Purpose of the Study:

• To test the predicted power law relationship between stimulus rate and activity in excitable lattices.
• To investigate the influence of dimensionality on the response exponent.
• To explore how self-sustained activity affects network response and dynamic range.

Main Methods:

• Modeling excitable lattices using coupled Morris-Lecar equations and Greenberg-Hastings cellular automata.
• Analyzing the response function F(h) in the low-stimulus regime (h ≈ 0).
• Investigating the impact of lattice dimensionality (d=1, 2, 3) and conductance coupling (G) on network dynamics.

Main Results:

• The predicted power law F(h) ≈ h^m with m=1/(1+d) was verified for d=1, 2, and 3 under specific conditions.
• Dynamic range increased with dimensionality when the power law held.
• The power law scenario failed when self-sustained activity (spiral waves) emerged, with dynamic range peaking at a critical coupling G_c.

Conclusions:

• Dimensionality plays a significant role in shaping the response of excitable networks to stimuli.
• Self-sustained activity introduces a critical transition point that alters network coding capabilities.
• These findings have implications for understanding information processing in biological neural networks.