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A modified van der Pol equation with delay in a description of the heart action

Beata Zduniak;  Marek Bodnar;  Urszula Foryś — 2014

International Journal of Applied Mathematics and Computer Science

In this paper, a modified van der Pol equation is considered as a description of the heart action. This model has a number of interesting properties allowing reconstruction of phenomena observed in physiological experiments as well as in Holter electrocardiographic recordings. Our aim is to study periodic solutions of the modified van der Pol equation and take into consideration the influence of feedback and delay which occur in the normal heart action mode as well as in pathological modes. Usage...

Dynamics of simplified HPT model in relation to 24h TSH profiles

Agnieszka Bartłomiejczyk;  Beata Jackowska-Zduniak — 2018

Mathematica Applicanda

We propose a simplified mathematical model of the hypothalamus-pituitary-thyroid (HPT) axis in an endocrine system. The considered model is a modification of the model proposed by Mukhopadhyay in [9]. Our system of delay differential equations reconstructs the HPT-axis in relation to 24h profiles of human in physiological conditions. Homeostatic control of the thyroid-pituitary axis is considered by using feedback and delay in our model. The influence of delayed feedback on the stability behaviour...

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