Investigation of Zeeman Models with Time Delays
Pinar Oral
Department of Mathematical Engineering, Gümüşhane University, Gümüşhane, Turkey.
Mehmet Merdan *
Department of Mathematical Engineering, Gümüşhane University, Gümüşhane, Turkey.
Zafer Bekiryazici
Department of Mathematics, Recep Tayyip Erdogan University, Rize, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the stability of the equilibrium points of the two dimensional Zeeman Heartbeat Model is investigated with time delay in cardiac muscle fiber or stimulator. The formulation of the heartbeat model is explained in the first part. Then, the stability conditions for the equilibrium points of the system are derived. Finally, some examples are given to illustrate the results of the study. The overall objective of this study is to investigate the effects of time delays on the dynamics of the Zeeman Heartbeat Model.
Keywords: Zeeman Heartbeat model, time delay, stability, equilibrium.