scholarly journals Border collision bifurcation control of cardiac alternans

2005 ◽  
Author(s):  
M.A. Hassouneh ◽  
E.H. Abed
Keyword(s):  
Bifurcation Control ◽  
Border Collision Bifurcation ◽  
Cardiac Alternans

scholarly journals Cardiac Alternans Arising From an Unfolded Border-Collision Bifurcation

2008 ◽  
Vol 3 (4) ◽  
pp. 041004 ◽  
Author(s):  
Xiaopeng Zhao ◽  
David G. Schaeffer ◽  
Carolyn M. Berger ◽  
Wanda Krassowska ◽  
Daniel J. Gauthier
Keyword(s):  
Border Collision Bifurcation ◽  
Cardiac Alternans

Cardiac Alternans Arising From an Unfolded Border-Collision Bifurcation

2007 ◽  
Author(s):  
Xiaopeng Zhao ◽  
David G. Schaeffer ◽  
Carolyn M. Berger ◽  
Wanda Krassowska ◽  
Daniel J. Gauthier
Keyword(s):  
Action Potential ◽  
Cardiac Tissue ◽  
Medical Literature ◽  
Period Doubling ◽  
Electrical Stimulus ◽  
Period Doubling Bifurcation ◽  
Small Interval ◽  
Border Collision Bifurcation ◽  
Transmembrane Voltage ◽  
Cardiac Alternans

Following an electrical stimulus, the transmembrane voltage of cardiac tissue rises rapidly and remains at a constant value before returning to the resting value, a phenomenon known as an action potential. When the pacing rate of a periodic train of stimuli is increased above a critical value, the action potential undergoes a period-doubling bifurcation, where the resulting alternation of the action potential duration is known as alternans in the medical literature. In principle, a period-doubling bifurcation may occur through either a smooth or a nonsmooth mechanism. Previous experiments reveal that the bifurcation to alternans exhibits hybrid smooth/nonsmooth behaviors, which is due to large variations in the system’s properties over a small interval of bifurcation parameter. To reproduce the experimentally observed hybrid behaviors, we have developed a model of alternans that exhibits an unfolded border-collision bifurcation. Excellent agreement between simulation of the model and experimental data suggests that features of the unfolded border-collision model should be included in modeling cardiac alternans.

scholarly journals BORDER COLLISION BIFURCATION CONTROL OF CARDIAC ALTERNANS

2004 ◽  
Vol 14 (09) ◽  
pp. 3303-3315 ◽  
Author(s):  
MUNTHER A. HASSOUNEH ◽  
EYAD H. ABED
Keyword(s):  
Period Doubling ◽  
Region Of Interest ◽  
Period Doubling Bifurcation ◽  
Cardiac Conduction ◽  
Parameter Region ◽  
Conduction Model ◽  
Control Laws ◽  
Border Collision Bifurcation ◽  
Cardiac Alternans ◽  
Smooth System

The quenching of alternans is considered using a nonlinear cardiac conduction model. The model consists of a nonlinear discrete-time piecewise smooth system. Several authors have hypothesized that alternans arise in the model through a period-doubling bifurcation. In this work, it is first shown that the alternans exhibited by the model actually arise through a period-doubling border collision bifurcation. No smooth period-doubling bifurcation occurs in the parameter region of interest. Next, recent results of the authors on feedback control of border collision bifurcation are applied to the model, resulting in control laws that quench the bifurcation, and hence result in alternan suppression.

scholarly journals The Mechanisms of Calcium Cycling and Action Potential Dynamics in Cardiac Alternans

2015 ◽  
Vol 116 (5) ◽  
pp. 846-856 ◽  
Author(s):  
Giedrius Kanaporis ◽  
Lothar A. Blatter
Keyword(s):  
Action Potential ◽  
Calcium Cycling ◽  
Cardiac Alternans

Stability analysis and bifurcation control of generalized phytoplankton-zooplankton system

2011 ◽  
Author(s):  
Qingling Zhang ◽  
Yugen Chang ◽  
Hong Niu ◽  
Chao Liu
Keyword(s):  
Stability Analysis ◽  
Bifurcation Control

scholarly journals B-PO02-026 LOCALIZED CARDIAC ALTERNANS PRESAGE VENTRICULAR TACHYARRHYTHMIAS IN OVINE CHRONIC MYOCARDIAL INFARCTION MODEL

Heart Rhythm ◽  
2021 ◽  
Vol 18 (8) ◽  
pp. S105-S106
Author(s):  
Kanchan Kulkarni ◽  
Nestor Pallares-Lupon ◽  
Virginie Loyer ◽  
Stephane Bloquet ◽  
Dounia El Hamrani ◽  
...  
Keyword(s):  
Myocardial Infarction ◽  
Chronic Myocardial Infarction ◽  
Ventricular Tachyarrhythmias ◽  
Cardiac Alternans

LOCAL AND GLOBAL BIFURCATIONS IN THREE-DIMENSIONAL, CONTINUOUS, PIECEWISE SMOOTH MAPS

2011 ◽  
Vol 21 (06) ◽  
pp. 1617-1636 ◽  
Author(s):  
SOMA DE ◽  
PARTHA SHARATHI DUTTA ◽  
SOUMITRO BANERJEE ◽  
AKHIL RANJAN ROY
Keyword(s):  
Three Dimensional ◽  
Global Bifurcation ◽  
Period Doubling ◽  
Piecewise Smooth ◽  
Numerical Continuation ◽  
Homoclinic Tangency ◽  
Global Dynamics ◽  
Global Bifurcations ◽  
Border Collision Bifurcation ◽  
Smooth Map

In this work, we study the dynamics of a three-dimensional, continuous, piecewise smooth map. Much of the nontrivial dynamics of this map occur when its fixed point or periodic orbit hits the switching manifold resulting in the so-called border collision bifurcation. We study the local and global bifurcation phenomena resulting from such borderline collisions. The conditions for the occurrence of nonsmooth period-doubling, saddle-node, and Neimark–Sacker bifurcations are derived. We show that dangerous border collision bifurcation can also occur in this map. Global bifurcations arise in connection with the occurrence of nonsmooth Neimark–Sacker bifurcation by which a spiral attractor turns into a saddle focus. The global dynamics are systematically explored through the computation of resonance tongues and numerical continuation of mode-locked invariant circles. We demonstrate the transition to chaos through the breakdown of mode-locked torus by degenerate period-doubling bifurcation, homoclinic tangency, etc. We show that in this map a mode-locked torus can be transformed into a quasiperiodic torus if there is no global bifurcation.

scholarly journals Chaotic dynamics of a pulse modulated control system for a heating unit

2018 ◽  
Vol 224 ◽  
pp. 02055
Author(s):  
Yuriy A. Gol’tsov ◽  
Alexander S. Kizhuk ◽  
Vasiliy G. Rubanov
Keyword(s):  
Control System ◽  
Differential Equations ◽  
Chaotic Dynamics ◽  
Period Doubling ◽  
Classical Period ◽  
Nonlinear Phenomena ◽  
Pulse Control ◽  
Heating Unit ◽  
Border Collision Bifurcation ◽  
Period Doubling Bifurcations

The dynamic modes and bifurcations in a pulse control system of a heating unit, the condition of which is described through differential equations with discontinuous right–hand sides, have been studied. It has been shown that the system under research can demonstrate a great variety of nonlinear phenomena and bifurcation transitions, such as quasiperiodicity, multistable behaviour, chaotization of oscillations through a classical period–doubling bifurcations cascade and border–collision bifurcation.

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