This letter discusses a behavior of solitons in a Josephson junction transmission line which is described by a perturbed sine-Gordon equation. It is shown that a soliton wave leads a quasi-periodic break down route to chaos in a Josephson transmission line. This route show phase locking, quasi-periodic state, chaos and hyper chaos, and these phenomena are examined by using Poincar sections, circle map, rotation number, and so on.

Various models of a neuron have been proposed and many studies about them and their networks have been reported. Among these neurons, this paper describes a study about the model of a neuron providing its own feedback input and possesing a chaotic dynamics. Using a return map or a histogram of laminar length, type-I intermittency is recognized in a recurrent neuron and its network. A posibility of controlling dynamics in recurrent neural networks is also mentioned a little in this paper.

This letter describes one neuron's dynamics. This neuron provides its own feedback input. We call this neuron the recurrent neuron and investigate its nonlinear dynamics.