Chaotifying delayed recurrent neural networks via impulsive effects

Area of Science:

• Dynamical Systems and Control Theory
• Artificial Intelligence
• Computational Neuroscience

Background:

• Recurrent neural networks (RNNs) with time delays are crucial for modeling complex systems.
• Understanding and controlling chaotic dynamics in these networks is an active research area.
• Impulsive control strategies offer a method for manipulating system behavior.

Purpose of the Study:

• To investigate the chaotification of delayed recurrent neural networks.
• To introduce a novel method using chaotically changing moments of impulsive actions.
• To establish theoretical conditions for achieving specific chaotic behaviors.

Main Methods:

• Theoretical analysis based on Lyapunov stability theory and bifurcation analysis.
• Derivation of sufficient conditions for Li-Yorke chaos.
• Inclusion of proximality, frequent separation, and existence of infinitely many periodic solutions.
• Numerical simulations to validate the theoretical results.

Main Results:

• Sufficient conditions for the presence of Li-Yorke chaos in delayed RNNs are theoretically established.
• The proposed method effectively induces chaotic dynamics through impulsive actions.
• The study confirms the existence of proximality, frequent separation, and infinitely many periodic solutions.

Conclusions:

• The chaotification of delayed recurrent neural networks is achievable using chaotically modulated impulsive actions.
• The theoretical framework provides a rigorous basis for understanding and controlling chaos in such systems.
• Numerical evidence supports the efficacy of the proposed chaotification strategy.