Numerical analyses and experimental validations of coexisting multiple attractors in Hopfield neural network

By simplifying connection topology of Hopfield neural network (HNN) with three neurons, a kind of HNN-based nonlinear system is proposed. Taking a coupling-connection weight as unique adjusting parameter and utilizing conventional dynamical analysis methods, dynamical behaviors with the variation of the adjusting parameter are discussed and coexisting multiple attractors' behavior under different state initial values are investigated. The results imply that the HNN-based system displays point, periodic, and chaotic behaviors as well as period-doubling and tangent bifurcation routes; particularly, this system exhibits some striking phenomena of coexisting multiple attractors, such as, a pair of single-scroll chaotic attractors accompanied with a pair of periodic attractors, a pair of periodic attractors with two periodicities, and so on. Of particular interest, it should be highly significant that a hardware circuit of the HNN-based system is developed by using commercially available electronic components and many kinds of coexisting multiple attractors are captured from the hardware experiments. The results of the experimental measurements have well consistency to those of MATLAB and PSpice simulations.