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

Synchronization phenomena in van der Pol oscillators coupled by a time-varying resistor

Abstract-In this study, synchronization phenomena observed in van der Pol oscillators coupled by a fifth-power nonlinear resistor are investigated. By carrying out computer simulations, interesting synchronization phenomena can be confirmed to be generated in this system. Namely, the synchronization states change according to the coupling strength and nonlinearity of the coupling resistor

Numerical Simulation

Nowadays mathematical modeling and numerical simulations play an important role in life and natural science. Numerous researchers are working in developing different methods and techniques to help understand the behavior of very complex systems, from the brain activity with real importance in medicine to the turbulent flows with important applications in physics and engineering. This book presents an overview of some models, methods, and numerical computations that are useful for the applied research scientists and mathematicians, fluid tech engineers, and postgraduate students