Multiperiodicity and exponential attractivity evoked by periodic external inputs in delayed cellular neural networks

Area of Science:

• Computational Neuroscience
• Dynamical Systems Theory
• Nonlinear Systems Analysis

Background:

• Cellular Neural Networks (CNNs) are crucial for signal processing.
• Understanding the stability and dynamics of CNNs with time delays is essential.
• Existing models often lack comprehensive analysis of periodic orbits in saturation regions.

Purpose of the Study:

• To investigate the existence and properties of periodic orbits in n-neuron CNNs with time-varying delays.
• To establish conditions for local and global exponential attractiveness of these orbits.
• To extend the theory of exponential stability for delayed CNNs.

Main Methods:

• Analysis of nonlinear differential equations governing CNN dynamics.
• Application of stability theory for time-delay systems.
• Development of novel criteria for orbit attractiveness and localization.

Main Results:

• Identified 2(n) periodic orbits within saturation regions for CNNs with time-varying delays.
• Periodic orbits are proven to be locally exponentially attractive.
• Conditions derived for local/global exponential attractiveness and arbitrary region localization.

Conclusions:

• The study provides improved and extended results on the stability of delayed CNNs.
• The findings offer new insights into the complex dynamics of neural networks.
• Numerical simulations validate the theoretical conditions and demonstrate practical applicability.