Hysteresis Phenomena in Transitional Zones Between Various Kinds of Periodic and Quiescent Behaviour in Electrophysiological Mathematical Models of Cardiac Cells

  • M. Landau
Part of the NATO ASI Series book series (NSSB, volume 244)


This study deals with a mathematical model of a system composed of coupled pacemakers (PM) and non-pacemaker (NPM) cardiac cells, when electrical coupling resistance and pacemaker cell size are allowed to vary. Broad outlines of classification were provided by direct numerical simulation for discrete values of the parameters. For a large PM cell size, the NPM cell is always activated, showing either a sustained rhythmic activity or subthreshold oscillations. When PM cell size is reduced, we observe, in addition to these NPM cell responses, a complete inhibition of the system at low values of coupling resistance. Then we turn to the systematic study of these phenomena with the continuation techniques of stationary and periodic solutions and detection of Hopf bifurcation points. In this new qualitative behaviour appears for the system. In two zones of values of the coupling resistance coexist stationary and periodic stable states, or two stable periodic states of large and low amplitude.


Periodic Solution Direct Numerical Simulation Bifurcation Diagram Hysteresis Phenomenon Hopf Bifurcation Point 
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • M. Landau
    • 1
  1. 1.CNRS at INRIARocquencourtFrance

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