Complex mixed-mode periodic and chaotic oscillations in a simple three-variable model of nonlinear system

A detailed study of a generic model exhibiting new type of mixed-mode oscil lations is presented. Period doubling and various period adding sequences o f bifurcations are observed. New type of a family of 1D (one-dimensional) r eturn maps is found. The maps are discontinuous at three points and consist of four branches. They are not invertible. The model describes in a qualit ative way mixed-mode oscillations with two types of small amplitude oscilla tions at local maxima and local minima of large amplitude oscillations, whi ch have been observed recently in the Belousov-Zhabotinsky system. (C) 2000 American Institute of Physics. [S1054-1500(00)01102-2].