Rulkov neural network coupled with discrete memristors

Area of Science:

• Computational Neuroscience
• Nonlinear Dynamics
• Complex Systems

Background:

• Memristive-coupled neural networks are well-studied in continuous domains.
• Discrete domain characteristics of these networks are less explored.
• Rulkov neuron maps are a significant model for neuronal dynamics.

Purpose of the Study:

• To construct a discrete memristor with sine-type conductance.
• To investigate the properties of memristive-coupled Rulkov neuron maps in the discrete domain.
• To analyze the impact of parameters and coupling on system dynamics.

Main Methods:

• Development of a discrete memristor model with sine-type conductance.
• Application of the discrete memristor to couple Rulkov neuron maps (bi-neuron and multi-neuron networks).
• Utilizing numerical simulation techniques including normalized mean synchronization error, bifurcation diagrams, phase portraits, and spatiotemporal patterns.

Main Results:

• Successfully constructed and applied a discrete memristor to Rulkov neuron maps.
• Demonstrated that both system parameters and coupling factors significantly influence network dynamics.
• Observed complex and interesting behavioral changes in the discrete memristive-coupled neural networks.

Conclusions:

• The discrete memristor provides a new approach for modeling neural networks in the discrete domain.
• Parameter and coupling variations lead to rich and complex dynamics in these systems.
• This research opens avenues for exploring discrete memristive neural network behaviors.