Collective behavior of an adapting synapse-based neuronal network with memristive effect and randomness

Area of Science:

• Computational Neuroscience
• Complex Systems Dynamics
• Network Science

Background:

• Adaptive synapse neuron models are crucial for understanding brain function.
• Small-world networks, characterized by local clustering and short path lengths, are prevalent in biological systems.
• Electromagnetic flux and memristive synapses introduce complex dynamics and coupling mechanisms.

Purpose of the Study:

• To investigate the global multi-stability of a single adaptive synapse neuron model with magnetic flux.
• To analyze the dynamics and synchronization of two coupled neurons with a memristive synapse.
• To explore the collective behavior of neurons in a small-world network with varying parameters.

Main Methods:

• Numerical simulations using bifurcation plots, phase plots, and basin of attraction analysis.
• Analysis of coupled neuron dynamics via largest Lyapunov exponents and mean average error.
• Reconstruction of regular networks into small-world networks with controlled rewiring probability.

Main Results:

• Demonstration of global multi-stability in the single neuron model due to switchable equilibrium states.
• Observation of synchronized dynamics in coupled neurons.
• Identification of collective behavior in small-world networks influenced by neighborhood connections, coupling strength, and rewiring probability.

Conclusions:

• The adaptive synapse neuron model with magnetic flux exhibits complex dynamics and global multi-stability.
• Small-world network topology significantly impacts collective neuron behavior and synchronization.
• This research provides insights into the emergent properties of complex neural networks.