2020 Volume 13 Issue 3 Pages 187-196
From around 1960 to the 1980's, various biological phenomena attracted much attention and were intensively studied using nonlinear methematical models. Using several simplified neuron models, such as the Caianiello neuron and Nagumo-Sato models, and a model of a biological oscillator, as examples, we show that a common dynamics expressed by a one-dimensional discrete dynamical system (one-dimensional mapping) underlies such models arising in different biological contexts. In particular, exploration of the nonlinear dynamics of a piecewise linear mapping in detail shows that very complicated nonlinear phenomena can be generated by very simple nonlinear dynamics.