Implementation of the Classical Aihara Chaotic Neural Network Model

The Aihara chaotic neural network model is a classical mathematical framework for studying chaotic behavior in neural systems, with its core focus on revealing nonlinear dynamic characteristics in neuronal firing activities. This model employs discrete-time iterative equations to simulate chaotic oscillation phenomena exhibited by biological neurons under specific parameters.

Model construction primarily involves three key elements: The membrane potential update mechanism utilizes nonlinear transformation through hyperbolic tangent functions, which serves as the mathematical foundation for generating chaotic behavior The self-feedback connection weight parameter controls system stability - when exceeding critical values, the system enters chaotic states External input current acts as a bifurcation parameter, where variations trigger transitions from periodic oscillations to chaotic regimes

In typical implementations, two important characteristic behaviors are observed: Phase space reconstruction enables visualization of strange attractor trajectories resembling Lorenz attractors Lyapunov exponent calculations quantitatively confirm the system's chaotic properties

The model's significance in neural computing lies in providing mathematical tools for understanding stochastic characteristics in brain information processing. Subsequent improved versions have been applied to intelligent algorithm designs including associative memory and optimization computing. Parameter adjustment strategies and stability analysis represent critical technical considerations for practical applications.