The safe basin of a forced softening Duffing oscillator is studiednumerically. The changes of safe basins are observed under bothstationary and nonstationary variations of the external excitationfrequency. The kind of...The safe basin of a forced softening Duffing oscillator is studiednumerically. The changes of safe basins are observed under bothstationary and nonstationary variations of the external excitationfrequency. The kind of nonstationary variations of the excitationfrequency can greatly change the erosion rate and the shape of thesafe basin. The other effects of nonstatinary variations on the safebasin are also discussed.展开更多
This paper considers the dynamical behavior of a Duffing-Mathieu type system with a cubic single-well potential during the principal parametric resonance. Both the cases of constant and time-dependent excitation ampli...This paper considers the dynamical behavior of a Duffing-Mathieu type system with a cubic single-well potential during the principal parametric resonance. Both the cases of constant and time-dependent excitation amplitude are used to observe the variation of the extent and the rate of the erosion in safe basins. It is evident that the appearance of fractal basin boundaries heralds the onset of the losing of structural integrity. The minimum value of control parameter to prevent the basin from erosion is given along with the excitation amplitude varying. The results show the time-dependence of excitation amplitude can be used to control the extent and the rate of the erosion and delay the first occurrence of heteroclinic tangency.展开更多
基金the National Natural Science Foundationthe Aviation S■ loundationthe Doctoral Training Foundation of China
文摘The safe basin of a forced softening Duffing oscillator is studiednumerically. The changes of safe basins are observed under bothstationary and nonstationary variations of the external excitationfrequency. The kind of nonstationary variations of the excitationfrequency can greatly change the erosion rate and the shape of thesafe basin. The other effects of nonstatinary variations on the safebasin are also discussed.
基金the National Science Foundation of ChinaPSF of China
文摘This paper considers the dynamical behavior of a Duffing-Mathieu type system with a cubic single-well potential during the principal parametric resonance. Both the cases of constant and time-dependent excitation amplitude are used to observe the variation of the extent and the rate of the erosion in safe basins. It is evident that the appearance of fractal basin boundaries heralds the onset of the losing of structural integrity. The minimum value of control parameter to prevent the basin from erosion is given along with the excitation amplitude varying. The results show the time-dependence of excitation amplitude can be used to control the extent and the rate of the erosion and delay the first occurrence of heteroclinic tangency.
