Fractal variation of attractors in complex-valued neural networks

摘要

Fractal variation of dynamical attractors is observed in complex-valued neural networks where a negative-resistance nonlinearity is introduced as the neuron nonlinear function. When a parameter of the negative-resistance nonlinearity is continuously changed, it is found that the network attractors present a kind of fractal variation in a certain parameter range between deterministic and non-deterministic attractor ranges. The fractal pattern has a convergence point, which is also a critical point where deterministic attractors change into chaotic attractors. This result suggests that the complex-valued neural networks having negative-resistance nonlinearity present the dynamics complexity at the so-called edge of chaos.