Dynamical System with Multi-Delays Mathematical Models.

      Аннотация: To obtain a deep and clear understanding of dynamical systems of cardiovascular- respiratory system the interesting way is to investigate delay models [30]. The problem was that the presence of multi-delays causes the complexity of determining the bifurcation points. This work was undertaken in order to determine the Hopf bifurcation points of the cardiovascular respiratory mathematical model with two delays, where in the numerical simulation we consider a 30 years old woman in the physical activities such as walking, jogging, running fast. The algorithm was developed to overcome the difficulties of finding the Hopf bifurcation points of multiple delay models. We focused on linearization of two delays mathematical model around the equilibrium points and the numerical simulations based on the theory of alpha -dense curve we tried to find out the general algorithm. The findings results show that a small perturbation of Hopf bifurcation parameters allows a state to pass from stable state by passing through on an intermediate transition phase to unstable state in all these three considered physical activities.

Ключевые слова: linearization, Hopf bifurcation, ?-dense curve, delay models, critical points