HYPERCHAOS IN ACETYLCHOLINESTERASE ENZYME-SYSTEMS

Burst generation via a complex bifurcation scenario is discussed using a two compartments model of an enzyme system with substrate inhibitio n kinetics affected by the production of hydrogen ions accompanying th e reaction (e.g. acetylcholinesterase enzyme system). Evidences are gi ven to support the existence of homoclinicity associated with this com plex dynamics, including the generalised criterion developed by Rossle r er al. [1] for the application of Sil'nikov's theorem in the case of four-dimensional systems. Complex bi-stabilities are observed in cert ain regions, and the structure of some attracting sets occurring near homoclinic orbits are discussed. The results support the use of such f undamental models for different dynamical modes generation and analysi s. The results relate to the transition of small and large frequency o scillations to periodic bursting and vice versa in excitable cells and many biophysical systems. (C) 1997 Elsevier Science Ltd.