Abstract: We propose a three-neuron heterogeneous cyclic Hopfield neural network (het-CHNN) utilizing three different activation functions: the hyperbolic tangent, sine, and cosine functions. The network’s globally uniformly ultimate boundedness is proved theoretically, and its chaotic dynamics are explored through numerical simulations and analog experiments. The numerical results demonstrate that the het-CHNN displays chaotic dynamics and multi-scroll chaotic attractors. Subsequently, the het-CHNN is implemented in an analog circuit, and hardware experiments are performed to verify the previous numerical results. Notably, the het-CHNN successfully resolves the issue of the absence of chaos in a three-neuron CHNN and currently appears to be the simplest three-neuron Hopfield neural network (HNN) that can generate chaos.

Key words: Activation function; Analog circuit; Chaos; Cyclic Hopfield neural network (CHNN); Multi-scroll chaotic attractor

Please provide your name, email address and a comment

Your Name: Affili: E-Mail Address:

Comment (Please comment in English):


Verification Code(click to change a pic):