Generalization Of Neural Networks To The Complex Plane

A complex-valued generalization of neural networks is presented. The dynamics of complex neural networks have parallels in discrete complex dynamics which give rise to the Mandelbrot set and other fractals. The continuation to the complex plane of common activation functions and the resulting neural dynamics are discussed. An activation function with more desirable characteristics in the complex plane is proposed. The dynamics of this activation function include the possibility of self oscillation. Possible applications in signal processing and neurobiological modeling are discussed