Numerical Analysis of the Coupled Modified Van der Pol Equations in a Model of Heart Action
In this paper, modified van der Pol equations are considered as В 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 stable solutionsВ can be found. The physiological model works in nearest range of parameters and allows to obtain В stable behaviour which is important for В solving the biological problem. When some kinds of pathologies appear in the heart, it is possible to obtain a chaotic behaviour. В My aim is to compare the influence of two types of coupling (unidirectional and bidirectional) on the behaviour of the van der PolвЂ™s system. The coupling takes place in the healthy conductivity system between two nodes, SA and AV, but in some circumstances the pathological coupling can occur in the heart. The Van der Pol oscillator is a type of a relaxation oscillator, which can be synchronized. Synchronization properties of such a system is studied in the following work. For numerical analysis of the discussed system a numerical model was created.
The journal Biomath Communications is an open access journal. All published articles are immeditely available online and the respective DOI link activated. All articles can be access for free and no reader registration of any sort is required. No fees are charged to authors for article submission or processing. Online publications are funded through volunteer work, donations and grants.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).