Bifurcation and nonlinear dynamic analysis of heart blood vessel system

Many studies have been shown and focused that variation of the quantity of vasoconstriction and blood pressure will cause the nonlinear chaotic behaviors in the heart blood vessel system and then induce the cardiovascular effect. Due to this kind of non-periodic motion is random and difficult to control, it is important to analyze and understand the status of dynamic system under different parametric conditions. In this paper, the differential transformation method is used to investigate the governing equations of system, and the dynamic behavior is characterized by reference to bifurcation diagrams, phase portraits, power spectra, and Poincaré map produced. The results indicate that the system behavior is significantly dependent on the magnitude of the vibrational amplitude. Specifically, the motion changes from T-periodic to 2T-periodic, then from 4T-periodic to 8-periodic, and finally to chaotic motion with windows of periodic motion as the vibrational amplitude is increased from 0.3 to 0.6. The results can be used as the basis for subsequent development of the control system design, and also reduced the possibility of cardiopathy.