In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and ...In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays.展开更多
In this paper, an index for evaluating Distance of a healthy heart from Sino-Atrial Blocking Arrhythmia (SABA) is presented. After definition of the main pacemakers' model of heart, Sino-Atrial (SA) and Atrio-Vent...In this paper, an index for evaluating Distance of a healthy heart from Sino-Atrial Blocking Arrhythmia (SABA) is presented. After definition of the main pacemakers' model of heart, Sino-Atrial (SA) and Atrio-Ventricular nodes (AV), the boundary of synchronization, which demonstrates the boundary of blocking arrhythmia, is obtained using perturbation method. In order to estimate of healthy heart characteristics, a parameter estimator is introduced. The distance from SABA is calculated using Lagrange method and Kohn-Tucker conditions. In addition, the maximum admissible decrease in the coupling intensity and the maximum admissible increase in the discrepancy between the natural frequencies of two pacemakers are determined in order to maintain the synchronization between the two pacemakers.展开更多
文摘In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays.
文摘In this paper, an index for evaluating Distance of a healthy heart from Sino-Atrial Blocking Arrhythmia (SABA) is presented. After definition of the main pacemakers' model of heart, Sino-Atrial (SA) and Atrio-Ventricular nodes (AV), the boundary of synchronization, which demonstrates the boundary of blocking arrhythmia, is obtained using perturbation method. In order to estimate of healthy heart characteristics, a parameter estimator is introduced. The distance from SABA is calculated using Lagrange method and Kohn-Tucker conditions. In addition, the maximum admissible decrease in the coupling intensity and the maximum admissible increase in the discrepancy between the natural frequencies of two pacemakers are determined in order to maintain the synchronization between the two pacemakers.
