ORGANIZING CENTERS AND SYMBOLIC DYNAMIC IN THE STUDY OF MIXED-MODE OSCILLATIONS GENERATED BY MODELS OF BIOLOGICAL AUTOCATALYTIC PROCESSES

The organization of the complex mixed-mode oscillations generated, in a three-dimensional variable space, by an autocatalytic process formal ized as a cubic monomial is analyzed. The generation of the temporal p atterns is elucidated by complementary approaches dealing with the thr ee-variable differential continuous system itself and with successive discrete applications modelling its first return map. The extent to wh ich the underlying bifurcation structures could constitute a fingerpri nt of autocatalytic processes is discussed in connection with the mode lling of biological systems.