Numerical Analysis of the Coupled Modified van der Pol Equations in a Model of Heart Action
In this paper, a modified van der Pol equations are considered as a description of the heart action. Wide ranges of the model parameters yield interesting qualitative results, e.g. Hopf bifurcation, Bogdanov-Takens bifurcation, transcritical and pitchfork bifurcations but also some stable solutions can be found. The physiological model works in the narrowest range of parameters which allows to obtain a stable behaviour what is important in biological problem. When some kinds of pathologies appear in the heart, it is possible to obtain chaotic behaviour. My aim is to compare the influence of these two types of coupling (unidirectional and bidirectional) on the behaviour of the van der Pol system. The coupling takes place in a system with healthy conductivity, between two nodes: SA and AV, but in some circumstances, a pathological coupling may occur in the heart. The van der Pol oscillator is a type of relaxation oscillator which can be synchronized. In this paper, synchronization properties of such a system are studied as well. For the purpose of a numerical analysis of the system in question, a numerical model was created.
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