Synchronization regimes for two coupled noisy Liénard-type driven oscillators

Santos, Ângela Maria dos; Lopes, S. R.; Viana, Ricardo L.

doi:10.1016/j.chaos.2006.07.019

Cited by 6 publications

(4 citation statements)

References 11 publications

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“…The synchronism between the three oscillators depends on the coupling coefficients K [35,36]. A lot of coupling methods can be found in the literature [37][38][39]. However, it is possible to avoid the use of delays τ n in the coupling terms by choosing the appropriate coupling coefficients K SA−AV and K AV−HP .…”

Section: Mathematical Modelmentioning

confidence: 99%

Improvement of the Cardiac Oscillator Based Model for the Simulation of Bundle Branch Blocks

et al. 2019

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In this paper, we propose an improvement of the cardiac conduction system based on three modified Van der Pol oscillators. Each oscillator represents one of the components of the heart conduction system: Sino-Atrial node (SA), Atrio-Ventricular node (AV) and His–Purkinje system (HP). However, while SA and AV nodes can be modelled through a single oscillator, the modelling of HP by using a single oscillator is a rough simplification of the cardiac behaviour. In fact, the HP bundle is composed of Right (RB) and Left Bundle (LB) branches that serve, respectively, the right and left ventricles. In order to describe the behaviour of each bundle branch, we build a phenomenological model based on four oscillators: SA, AV, RB and LB. For the characterization of the atrial and ventricular muscles, we used the modified FitzHugh–Nagumo (FHN) equations. The numerical simulation of the model has been implemented in Simulink. The simulation results show that the new model is able to reproduce the heart dynamics generating, besides the physiological signal, also the pathological rhythm in case of Right Bundle Branch Block (RBBB) and Left Bundle Branch Block (LBBB). In particular, our model is able to describe the communication interruption of the conduction system, when one of the HP bundle branches is damaged.

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Section: Mathematical Modelmentioning

confidence: 99%

Improvement of the Cardiac Oscillator Based Model for the Simulation of Bundle Branch Blocks

et al. 2019

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“…Lemma 3 lets us establish the following result. Theorem 4 Consider system (6). For each pair (D, δ), where D ⊂ R 2 is a compact convex set that does not include the origin and δ > 0, there exists ω * > 0 such that for all ω ≥ ω * the following hold.…”

Section: Synchronization Of Lienard Oscillatorsmentioning

confidence: 99%

“…We let the individual oscillators share identical dynamics and the coupling between them be nonlinear. We consider Lienard-type oscillators that have been much studied due to their close relation to real-life systems and applications [1,6,16]. A particular example is van der Pol oscillator [7,11].…”

Section: Introductionmentioning

confidence: 99%