Key result
Blood flow modeling shows asymptotic stability below a critical delay parameter and Hopf-bifurcation above it.
Why the study?
Conditions such as hypotension, atherosclerosis, or vascular resistance can cause a delay in blood passage from arteries to capillaries, prompting mathematical modeling of this delay in human blood flow dynamics.
Mathematical modeling demonstrates that delays in blood flow from arteries to capillaries can lead to Hopf-bifurcation and limit cycles, providing theoretical insights into circulatory dynamics.
No clinical implications; leaves open whether delay-induced bifurcations occur in human circulation.
The blood flow dynamics in the human circulatory system , where blood passes through various arteries, capillaries and veins is realistically modelled in this research paper. Several physiological, pathological, or environmental conditions might cause a delay in the passage of blood from arteries to capillaries such as hypotension, atherosclerosis , vascular resistance etc. This delay has been incorporated in this mathematical model. Feasible non-zero equilibrium is calculated and the stability analysis is carried about this equilibrium point. The asymptotic stability is seen for below-critical point value of delay parameter. Hopf-bifurcation through limit cycles is observed when value of delay parameter crosses the critical point. The analytical results are supported by numerical simulation using MATLAB and play a significant role in good health and well-being.
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Dipesh et al. (2025) studied Blood flow dynamics. Mathematical modeling with delay differential equations was evaluated on Stability analysis and Hopf-bifurcation. A mathematical model of blood flow dynamics showed asymptotic stability below a critical delay parameter and Hopf-bifurcation through limit cycles when the delay parameter crossed the critical point.
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