Averaged modeling of the cardiovascular system

In approximating nonlinear systems, averaging theory provides very useful tools, especially for periodic/quasi-periodic systems. In the case of complex dynamical systems (e.g. biological systems), such an approach leads to consistent simplifications of the encountered mathematical models. The current paper addresses the problem of deriving a simple averaged model of the cardiovascular system, which is shown to be part of the class of pulse-frequency modulated switched systems. Because conventional averaging methods lead to frequency independent averaged models, the paper proposes a weighted averaging approach, which leads to a frequency dependent averaged model (simpler than the original one).