Abstract
Two types of coronary artery system N‐type and S‐type, are investigated. The threshold conditions for the occurrence of Smale horseshoe chaos are obtained by using Melnikov method. Numerical simulations including phase portraits, potential diagram, homoclinic bifurcation curve diagrams, bifurcation diagrams, and Poincaré maps not only prove the correctness of theoretical analysis but also show the interesting bifurcation diagrams and the more new complex dynamical behaviors. Numerical simulations are used to investigate the nonlinear dynamical characteristics and complexity of the two systems, revealing bifurcation forms and the road leading to chaotic motion. Finally the chaotic states of the two systems are effectively controlled by two control methods: variable feedback control and coupled feedback control.
Highlights
Chaotic science is one of the three major scientific achievements in 20th century
The coronary artery system driven by periodic excitations is a typical nonlinear vibration system and has a rich dynamic behavior
From the mathematical point of view, the vascular spasm is the chaotic state of vasomotor
Summary
Since the Lorenz system was discovered in 1963, many new chaotic systems have been successively raised 1–4. The proposal of these systems promotes the theory research of chaos to continue indepth and provides supports for the application of chaos in the field of engineering technology, for example, information processes, secure communication. The model of coronary artery system and its chaotic motion were given in 9 , and by using Melnikov method the conditions for chaos of the two types are shown. There has been less attention to chaos control of the coronary artery system in all kinds of literatures, as a major topic of control science, it is necessary to investigate in detail. The chaos of the system 1.3 and 1.6 is controlled to stable periodic orbits by two kinds of control methods.
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