Locally active memristor-based Chialvo neuron model: bifurcation, multistability, and noise effects

Area of Science:

• Computational Neuroscience
• Nonlinear Dynamics
• Memristive Systems

Background:

• The Chialvo neuron model is a fundamental tool for studying neural dynamics.
• Memristors offer unique properties like nonvolatility and local activity, promising for complex system modeling.
• Understanding multistability and diverse firing patterns is crucial for neural computation.

Purpose of the Study:

• To propose a new memristive Chialvo neuron map by integrating a discrete memristor.
• To analyze the impact of memristor properties on neuron dynamics, stability, and multistability.
• To investigate the emergence of complex firing behaviors like chaos and the influence of noise.

Main Methods:

• Incorporation of a locally active discrete memristor into the Chialvo neuron model.
• Analysis of equilibrium points and their stability concerning memristive coupling strength.
• Dynamical analysis using bifurcation diagrams, largest Lyapunov exponents, and spectral entropy.
• Time-series and phase-space investigations, including the effect of stochastic perturbations.

Main Results:

• The memristive Chialvo model exhibits enhanced multistability with an increased number of equilibrium points.
• A wide range of firing behaviors (periodic, quasiperiodic, chaotic) were observed.
• Increasing memristive coupling generally suppresses chaotic regions but enriches oscillatory dynamics.
• The model shows bistability and multistability between distinct oscillatory attractors, dependent on initial conditions.
• Stochastic perturbations can induce spiking and bursting dynamics, with noise sensitivity decreasing at higher memristive coupling.

Conclusions:

• The proposed memristive Chialvo neuron map significantly enriches neural dynamics compared to the original model.
• The memristor integration enables complex phenomena like multistability and diverse firing patterns, crucial for advanced neural simulations.
• The model's response to noise highlights its potential for modeling real neural systems with inherent variability.