Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells

Science ◽  
1981 ◽  
Vol 214 (4527) ◽  
pp. 1350-1353 ◽  
Author(s):  
M. Guevara ◽  
L Glass ◽  
A Shrier
Keyword(s):  
Phase Locking ◽  
Period Doubling ◽  
Cardiac Cells ◽  
Period Doubling Bifurcations

Phase Locking, Period-Doubling Bifurcations, and Irregular Dynamics in Periodically Stimulated Cardiac Cells

2017 ◽  
pp. 178-184
Author(s):  
Michael Guevara ◽  
Leon Glass ◽  
Alvin Shrier
Keyword(s):  
Phase Locking ◽  
Period Doubling ◽  
Cardiac Cells ◽  
Period Doubling Bifurcations

scholarly journals Predicting the onset of period-doubling bifurcations in noisy cardiac systems

2015 ◽  
Vol 112 (30) ◽  
pp. 9358-9363 ◽  
Author(s):  
Thomas Quail ◽  
Alvin Shrier ◽  
Leon Glass
Keyword(s):  
Autocorrelation Function ◽  
Cardiac Arrhythmias ◽  
Social Systems ◽  
Period Doubling ◽  
Cardiac Cells ◽  
Autocorrelation Coefficient ◽  
Interbeat Interval ◽  
Return Map ◽  
Noise Amplification ◽  
Period Doubling Bifurcations

Biological, physical, and social systems often display qualitative changes in dynamics. Developing early warning signals to predict the onset of these transitions is an important goal. The current work is motivated by transitions of cardiac rhythms, where the appearance of alternating features in the timing of cardiac events is often a precursor to the initiation of serious cardiac arrhythmias. We treat embryonic chick cardiac cells with a potassium channel blocker, which leads to the initiation of alternating rhythms. We associate this transition with a mathematical instability, called a period-doubling bifurcation, in a model of the cardiac cells. Period-doubling bifurcations have been linked to the onset of abnormal alternating cardiac rhythms, which have been implicated in cardiac arrhythmias such as T-wave alternans and various tachycardias. Theory predicts that in the neighborhood of the transition, the system’s dynamics slow down, leading to noise amplification and the manifestation of oscillations in the autocorrelation function. Examining the aggregates’ interbeat intervals, we observe the oscillations in the autocorrelation function and noise amplification preceding the bifurcation. We analyze plots—termed return maps—that relate the current interbeat interval with the following interbeat interval. Based on these plots, we develop a quantitative measure using the slope of the return map to assess how close the system is to the bifurcation. Furthermore, the slope of the return map and the lag-1 autocorrelation coefficient are equal. Our results suggest that the slope and the lag-1 autocorrelation coefficient represent quantitative measures to predict the onset of abnormal alternating cardiac rhythms.

scholarly journals Can short time delays influence the variability of the solar cycle?

2010 ◽  
Vol 6 (S271) ◽  
pp. 288-296
Author(s):  
Laurène Jouve ◽  
Michael R. E. Proctor ◽  
Geoffroy Lesur
Keyword(s):  
Solar Cycle ◽  
Convection Zone ◽  
Mean Field ◽  
Period Doubling ◽  
Temporal Modulation ◽  
Solar Convection Zone ◽  
Flux Tubes ◽  
Solar Convection ◽  
Short Time ◽  
Period Doubling Bifurcations

AbstractWe present the effects of introducing results of 3D MHD simulations of buoyant magnetic fields in the solar convection zone in 2D mean-field Babcock-Leighton models. In particular, we take into account the time delay introduced by the rise time of the toroidal structures from the base of the convection zone to the solar surface. We find that the delays produce large temporal modulation of the cycle amplitude even when strong and thus rapidly rising flux tubes are considered. The study of a reduced model reveals that aperiodic modulations of the solar cycle appear after a sequence of period doubling bifurcations typical of non-linear systems. We also discuss the memory of such systems and the conclusions which may be drawn concerning the actual solar cycle variability.

Bifurcations and Chaos in a Minimal Neural Network: Forced Coupled Neurons

2021 ◽  
Vol 31 (10) ◽  
pp. 2150147
Author(s):  
Yo Horikawa
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Period Doubling ◽  
Output Function ◽  
Piecewise Constant ◽  
Border Collision Bifurcations ◽  
Saddle Node ◽  
Periodic Input ◽  
Symmetric Periodic Solution ◽  
Period Doubling Bifurcations

The bifurcations and chaos in a system of two coupled sigmoidal neurons with periodic input are revisited. The system has no self-coupling and no inherent limit cycles in contrast to the previous studies and shows simple bifurcations qualitatively different from the previous results. A symmetric periodic solution generated by the periodic input underdoes a pitchfork bifurcation so that a pair of asymmetric periodic solutions is generated. A chaotic attractor is generated through a cascade of period-doubling bifurcations of the asymmetric periodic solutions. However, a symmetric periodic solution repeats saddle-node bifurcations many times and the bifurcations of periodic solutions become complicated as the output gain of neurons is increasing. Then, the analysis of border collision bifurcations is carried out by using a piecewise constant output function of neurons and a rectangular wave as periodic input. The saddle-node, the pitchfork and the period-doubling bifurcations in the coupled sigmoidal neurons are replaced by various kinds of border collision bifurcations in the coupled piecewise constant neurons. Qualitatively the same structure of the bifurcations of periodic solutions in the coupled sigmoidal neurons is derived analytically. Further, it is shown that another period-doubling route to chaos exists when the output function of neurons is asymmetric.

Two Groups of Chaotic Vibrations in a Single-Degree-of-Freedom Maglev System

1997 ◽  
Author(s):  
Zhixiang Xu ◽  
Hideyuki Tamura
Keyword(s):  
Magnetic Levitation ◽  
Excitation Frequency ◽  
Power Spectra ◽  
Period Doubling ◽  
Excitation Amplitude ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Moving Base ◽  
Period Doubling Bifurcations

Abstract In this paper, a single-degree-of-freedom magnetic levitation dynamic system, whose spring is composed of a magnetic repulsive force, is numerically analyzed. The numerical results indicate that a body levitated by magnetic force shows many kinds of vibrations upon adjusting the system parameters (viz., damping, excitation amplitude and excitation frequency) when the system is excited by the harmonically moving base. For a suitable combination of parameters, an aperiodic vibration occurs after a sequence of period-doubling bifurcations. Typical aperiodic vibrations that occurred after period-doubling bifurcations from several initial states are identified as chaotic vibration and classified into two groups by examining their power spectra, Poincare maps, fractal dimension analyses, etc.

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.

scholarly journals Cascade of period doubling bifurcations and large stochasticity in the motions of a compass

1981 ◽  
Vol 42 (24) ◽  
pp. 537-539 ◽  
Author(s):  
V. Croquette ◽  
C. Poitou
Keyword(s):  
Period Doubling ◽  
Period Doubling Bifurcations
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