Experimental analysis of behavior stability in neuron gain domain in recurrent complex-valued neural networks

Behavior stability of recurrent complex-valued neural networks having dynamic output signals is investigated. The Lyapunov exponent is measured for a single-layer recurrent network when the signal-amplitude gain of neurons is varied. Time-sequential output signals are also presented for elucidating what happens in the network. It is found in the experiment that the network has a wide range of stably dynamic behavior in the gain domain where a phase-directional motive force governs the dynamics. This phenomenon is in a contrast to the behavior of conventional recurrent networks having dynamic signals generated by the information geometry in real-number space. The result suggests that the recurrent complex-valued networks are more useful for a stably dynamic information processing such as oscillation, waveform synthesis and adaptive filtering than conventional networks