Abstract
The organization of the complex mixed-mode oscillations generated, in a three-dimensional variable space, by an autocatalytic process formalized as a cubic monomial is analyzed. The generation of the temporal patterns is elucidated by complementary approaches dealing with the three-variable differential continuous system itself and with successive discrete applications modelling its first return map. The extent to which the underlying bifurcation structures could constitute a fingerprint of autocatalytic processes is discussed in connection with the modelling of biological systems.
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Tracqui, P. Organizing centres and symbolic dynamic in the study of mixed-mode oscillations generated by models of biological autocatalytic processes. Acta Biotheor 42, 147–166 (1994). https://doi.org/10.1007/BF00709487
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DOI: https://doi.org/10.1007/BF00709487