Simple trigonometric chaotic neuron models for associative memory neural networks

This paper presents simple trigonometric chaotic neuron models as a result from a search in the simplest internal nonlinear functions through the scan of positive Lyapunov Exponent (LE) bifurcation structures. The proposed chaotic neuron models are sine and cosine maps with a single input excitation and two arbitrary parameters, which are independent from the output activation function. Extensions to four simple cases of sine and cosine maps with complex chaotic dynamics are also investigated based on basic algebraic operations. Dynamics behaviors are demonstrated through bifurcation diagrams and LE spectrums. An application in associative memories of binary patterns in Cellular Neural Networks (CNN) topology is demonstrated using a signum output activation function. Three memory patterns are stored using symmetric auto-associative matrix of n binary patterns. Simulation results have shown that the CNN can quickly and effectively restore the distorted pattern to the expected information.