Heart Nodal Escape under Large Slow Adaptation Current

Document Type : Original Article

Authors

Arab Academy for Science and Technology & Maritime Transports, Alexandria, Egypt

Abstract

This paper presents a study for the qualitative behavior of the heart under large slow adaptation current condition. Different responses including fixed point, periodic, quasi periodic and ultimately chaotic behaviors are detected and shown. The mathematical model used in detecting bifurcation is a three dimensional model with two embedded nonlinearities of the third and second order types. The bifurcations are detected in the parameter space as the point of the change of system structure stability (splitting of the equilibrium points). The importance of this study is that it helps in forecasting whether or not the heart is liable to heart attack within a pre-determined period.

[1]           Wolf, A, et. Al., “Determining Lyapunov Exponents from a Time Series”, Physica 16D, PP 285-317, 1985.
[2]           [2]  A. A. A. Nasser, M. I. Sobhy, and , E. A. Hosny, “ Maximum Dynamic Range of Bifurcations from Chua's Circuit”, IEEE Journal of Circuits, Systems, and Computers, 1993.
[3]           [3] K. Pyragas, “Predictable chaos in slightly perturbed unpredictable chaotic system”, Phys. Lett. A, V. 181,  P.203-210, 1993.
[4]           [4] S.E Green, J.M. Jenkins, and R.S Macdonald “A Stochastic Network Model of the Interaction Between Cardiac Rhythm and Artificial Pacemaker”, IEEE transactions on Biomedical Engineering PP 845-858, September 1993.
[5]           [5] Joseph D. Bronzino, “The Biomedical Engineering Handbook”, Second Edition.                                                                     Boca Raton: CRC Press LLC; 2000. Ch 11.
[6]           [6] M. Sedky, A. Nasser and N. Hamdy, “Control of Heart Fibrillation Using Chaotic Synchronization” Nineteenth National Radio Science Conference, Alexandria, March,19-21, 2002.
[7]           [7]  E. Elmadbouly, A. A. Nasser, F. Elesawy, and S. Helmy,”Fuzzy Logic Control of Chaotic Systems”, 7th Int. National Conf. on Eng. AEIC,7-10 April , 2003, Alazhar Univ. , Cairo, Egypt.
[8]           [8] Andrey Shilnikov , Marina Kolomiets “Methods of the Qualitative Theory for the   Hindmarsh–Rose Model”,  International Journal of Bifurcation and Chaos, Vol. 18, No. 8, 2141–2168, 2008.