Y. S. Fan and A. V. Holden, “Bifurcation, Bursting, Chaos and Crisis in the Rose-Hindmarsh Model for Neuronal Activity,” Chaos, Solitons and Fractals, Vol. 3, No. 4, 1993, pp. 439-449. doi:10.1016/0960-0779(93)90029-Z

has been cited by the following article:

• TITLE: Bifurcation Analysis of a Coupled Acetylcholinesterase/Choline Acetyltransferase Enzymes Neurocycle

  AUTHORS: Hamza M. Habib, G. Ibrahim, Osama Noman Saleh

  KEYWORDS: Neurocycle Modelling; Acetylcholinesterase/Choline Acetyltransferase; Bifurcation; Enzyme; Nonlinear Dynamics

  JOURNAL NAME: Advances in Chemical Engineering and Science, Vol.3 No.1, January 11, 2013

  ABSTRACT: A diffusion-reaction, two-compartment model was used to explore the bifurcation and chaotic behavior of acetylcholinesterase (AChE) and cholineacetyltransferase (ChAT) coupled enzymes system. The effects of hydrogen ion feed concentrations, choline (Ch) and acetylcholine (ACh) feed concentrations, as bifurcation parameters on the system performance are studied. It is found that hydrogen ions play an important role in creating potential differences through the plasma membranes. Detailed bifurcation analysis over a wide range of parameters is carried out in order to uncover some of the qualitative changes of the system such as hysteresis, multiplicity, Hopf bifurcation, boundary crises bifurcation, periodic transient, and other complex dynamics. Some of the obtained results relate to the phenomena occurring in the physiological experiments like periodic stimulation of neural cells and irregular functioning of acetylcholine receptors. The model depends on real kinetics expressions and parameters obtained from the literature, so the results can be used to direct more systematic research on cholinergic disorder.