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Literature DB >> 6195280

The heart as a system of coupled nonlinear oscillators.

Abstract

In various approximations the heart is considered as a system of coupled nonlinear oscillators which are characterized by their phase transition curve (PTC) only. The system exhibits many phenomena which are known from ECG recordings such as multi-level-Wenckebach periodicity, dissociation, induction or removal of a tachycardia by an extrasystole, pseudo-block and the gap phenomenon. All these can be discussed within the model on a quantitative level.

Entities: Disease

Mesh：

Year: 1983 PMID： 6195280 DOI： 10.1007/bf00275911

Source DB: PubMed Journal: J Math Biol ISSN： 0303-6812 Impact factor: 2.259

8 in total

1. Reconstruction of the electrical activity of cardiac Purkinje fibres.

Authors: R E McAllister; D Noble; R W Tsien
Journal: J Physiol Date: 1975-09 Impact factor: 5.182

2. A COMPUTER MODEL OF ATRIAL FIBRILLATION.

Authors: G K MOE; W C RHEINBOLDT; J A ABILDSKOV
Journal: Am Heart J Date: 1964-02 Impact factor: 4.749

3. A modification of the Hodgkin--Huxley equations applicable to Purkinje fibre action and pace-maker potentials.

Authors: D NOBLE
Journal: J Physiol Date: 1962-02 Impact factor: 5.182

4. Simple mathematical models with very complicated dynamics.

Authors: R M May
Journal: Nature Date: 1976-06-10 Impact factor: 49.962

5. Model of bidirectional interaction between myocardial pacemakers based on the phase response curve.

Authors: N Ikeda
Journal: Biol Cybern Date: 1982 Impact factor: 2.086

6. Difference equation model of the entrainment of myocardial pacemaker cells based on the phase response curve.

Authors: N Ikeda; H Tsuruta; T Sato
Journal: Biol Cybern Date: 1981 Impact factor: 2.086

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

Authors: M R Guevara; L Glass; A Shrier
Journal: Science Date: 1981-12-18 Impact factor: 47.728

8. Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: a theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias.

Authors: M R Guevara; L Glass
Journal: J Math Biol Date: 1982 Impact factor: 2.259

8 in total

6 in total

The heart as a system of coupled nonlinear oscillators.

1. Reconstruction of the electrical activity of cardiac Purkinje fibres.

2. A COMPUTER MODEL OF ATRIAL FIBRILLATION.

3. A modification of the Hodgkin--Huxley equations applicable to Purkinje fibre action and pace-maker potentials.

4. Simple mathematical models with very complicated dynamics.

5. Model of bidirectional interaction between myocardial pacemakers based on the phase response curve.

6. Difference equation model of the entrainment of myocardial pacemaker cells based on the phase response curve.

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

8. Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: a theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias.

1. Regular and chaotic behaviour of cardiac cells stimulated at frequencies between 2 and 20 Hz.

2. The primacy of rhythm: how discrete actions merge into a stable rhythmic pattern.

3. Fibrillation of a cardiac region and the tachycardia mode of a two-oscillator system.

4. Global bifurcations of a periodically forced nonlinear oscillator.

5. Effect of spontaneous movement on respiration in preterm infants.

6. Community structure and multi-modal oscillations in complex networks.