Chaos and fractals from a forced artificial neural cell

Chaos and fractal responses from an artificial neural cell stimulated by a periodic square wave are discussed. The dynamics are described by an autonomous equation, and the one-dimensional return map is derived explicitly. The relation between the exciting pulse-width τ₁, and the excited rate γ_e which is the number ratio of input pulses and output pulses investigated. Mathematical evidence for γ_e to be Cantor function for τ₁ is given. It corresponds to fractal responses. A condition for observable chaos generation in responses from the cell is proved. This condition is described only by parameters. Some of the theoretical results are verified by laboratory experiments