Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective...

Area of Science:

• Computational Neuroscience
• Chaos Theory
• Fractional Calculus

Background:

• Hopfield-type neural networks are fundamental models in artificial intelligence.
• Fractional-order dynamics and time delays introduce complex behaviors in neural systems.
• Understanding chaotic dynamics is crucial for analyzing complex systems.

Purpose of the Study:

• To propose a novel three-dimensional fractional-order Hopfield-type neural network with delay.
• To investigate the complex dynamics, including intermittent chaos, periodicity, and stability.
• To develop a state-observer-based synchronization method for these networks.

Main Methods:

• Theoretical analysis of the system's equilibrium point and stability.
• Numerical simulations including phase portraits, bifurcation diagrams, and Largest Lyapunov exponent calculation.
• Design of a state observer for synchronization.

Main Results:

• The proposed network exhibits a unique, unstable saddle point equilibrium.
• Intermittent chaos, periodicity, and stability phenomena were identified and confirmed.
• A successful synchronization method for time-delayed fractional-order Hopfield-type neural networks was demonstrated.

Conclusions:

• The novel fractional-order Hopfield network displays rich and complex dynamics.
• The proposed synchronization technique is effective for this class of networks.
• This research contributes to the understanding of advanced neural network models.