Mean Square Exponential Stability of Dynamic Memristor Neutral Stochastic Cellular Neural Networks With Time-Varying...

Area of Science:

• Computational Neuroscience
• Nonlinear Dynamics
• Stochastic Systems

Background:

• Dynamic memristor-neutral stochastic cellular neural networks (DM-NSDCNNs) offer advantages in the flux-charge domain, including zero steady-state power consumption.
• Memristor-based neural networks are crucial for advanced computation, but their stability analysis requires specialized techniques.
• Existing neural network analyses often focus on the voltage-current domain, limiting applicability to memristor-based systems.

Purpose of the Study:

• To investigate the mean square exponential stability of DM-NSDCNNs with time-varying delays.
• To develop novel stability analysis techniques tailored for memristor-based neural networks.
• To validate the proposed methods using numerical simulations for different memristor constitutive relations.

Main Methods:

• Analysis in the flux-charge domain, distinct from traditional voltage-current domain studies.
• Application of the comparison principle and reductio ad absurdum for piecewise linear memristor relations.
• Utilization of Lyapunov functional techniques for stochastic analysis with cubic nonlinear memristor relations.

Main Results:

• Derivation of stability criteria for DM-NSDCNNs with piecewise linear memristor constitutive relations.
• Establishment of stability criteria for DM-NSDCNNs with cubic nonlinear memristor constitutive relations.
• Numerical examples confirm the effectiveness and potential of the developed stability analysis techniques.

Conclusions:

• The proposed methods effectively determine the mean square exponential stability of DM-NSDCNNs.
• The flux-charge domain analysis provides a robust framework for memristor-based neural networks.
• The study advances the understanding and application of memristor-based neural network stability.