Stochastic resonance in a pulse neural network with a propagational time delay

Area of Science:

• Computational neuroscience
• Nonlinear dynamics
• Complex systems

Background:

• The FitzHugh-Nagumo model is a simplified mathematical model of excitable systems, often used to study neuronal firing.
• Stochastic resonance describes a phenomenon where a non-linear system's response to a weak periodic signal is enhanced by the addition of noise.
• Time delays are crucial in understanding signal propagation and network dynamics in biological systems.

Purpose of the Study:

• To investigate stochastic resonance in a coupled FitzHugh-Nagumo equation incorporating a propagational time delay.
• To analyze the conditions under which additive noise can induce deterministic firing in this system.
• To examine the influence of network size and noise intensity on system behavior and competitive dynamics.

Main Methods:

• Numerical simulations of the coupled FitzHugh-Nagumo equations with a propagational time delay.
• Analysis of system response to periodic input and additive noise.
• Varying parameters such as input frequency, time delay, coupling strength, and noise intensity.
• Examination of neuronal firing patterns and network activity.

Main Results:

• Deterministic firing was observed under specific parameter settings, demonstrating stochastic resonance.
• The system's firing behavior was found to be dependent on the number of neurons in the network.
• A network of two assemblies exhibited competitive behavior, modulated by noise intensity.
• The interplay between time delay, coupling, and noise was shown to be critical for inducing and controlling firing.

Conclusions:

• Stochastic resonance can induce deterministic firing in coupled FitzHugh-Nagumo systems with time delays.
• Network architecture and noise intensity significantly influence neuronal activity and lead to emergent behaviors like competition.
• The findings provide insights into noise-driven dynamics in complex neuronal networks.