Noise-driven switching between limit cycles and adaptability in a small-dimensional excitable network with balanced...

Area of Science:

• Computational neuroscience
• Complex systems dynamics
• Nonlinear dynamics

Background:

• The FitzHugh-Nagumo model is a simplified mathematical model of the neuron's action potential.
• Understanding the collective behavior of coupled neuronal systems is crucial for neuroscience.
• Multistability and noise-induced phenomena are key features in complex dynamical systems.

Purpose of the Study:

• To investigate the emergence of multistable oscillatory states in a globally coupled FitzHugh-Nagumo system with excitatory and inhibitory units.
• To analyze the effect of noise on state switching and firing patterns.
• To explore the adaptability of the system's output to external periodic input.

Main Methods:

• Utilized a system of globally coupled FitzHugh-Nagumo equations.
• Varied the ratio of excitatory to inhibitory units.
• Introduced external noise to the system.
• Analyzed oscillatory states, firing rates, and correlation patterns.

Main Results:

• Identified a specific ratio of excitatory and inhibitory units leading to multistable oscillatory states with distinct firing rates.
• Observed noise-driven switching between these multistable states.
• Demonstrated that the resulting firing patterns exhibit long-range correlations.
• Showcased input-dependent selection between higher and lower frequency oscillations, indicating adaptability.

Conclusions:

• The interplay between excitatory and inhibitory units in coupled FitzHugh-Nagumo systems can generate complex multistable dynamics.
• Noise plays a critical role in mediating transitions between states and shaping network activity.
• The system demonstrates adaptive capabilities, adjusting its output frequency based on external periodic forcing.