The problem of how to control chaos has attracted a great deal of attention. A simplemethod is to suppress chaos by periodic perturbations. This method has already beenapplied to nonautonomous systems in most studies,...The problem of how to control chaos has attracted a great deal of attention. A simplemethod is to suppress chaos by periodic perturbations. This method has already beenapplied to nonautonomous systems in most studies, but seldom is it used to treat the au-tonomous systems and cases without motion equations. Based on one-dimensional maps,展开更多
The equations of the asymmetrical periodic motion in a two- -of-freedom vibrating system with two rigid constraints are constructed analytically. Its Poincard mapping equation is established too. Periodic motions of t...The equations of the asymmetrical periodic motion in a two- -of-freedom vibrating system with two rigid constraints are constructed analytically. Its Poincard mapping equation is established too. Periodic motions of the system and their routes to chaos are also illustrated by numerical simulation. The ranges of the system excited frequency from periodic motions to chaotic motions are obtained. The chaotic motions of the system are shown by di- agrams of Poincarg mapping, phase portraits and diagrams of bifurcation. The chaos controlling methods by the addition of constant load and the addition of phase are dissertated and analyzed numerically by the numerical solu- tion. The chaos of the system is controlled by the two methods. The allowable range controlling variables and the steady orbits of the controlled system are obtained.展开更多
基金Project supported by the National Basic Research Project"Nonlinear Science"of Chinathe National Natural Science Foundation of China
文摘The problem of how to control chaos has attracted a great deal of attention. A simplemethod is to suppress chaos by periodic perturbations. This method has already beenapplied to nonautonomous systems in most studies, but seldom is it used to treat the au-tonomous systems and cases without motion equations. Based on one-dimensional maps,
基金supported by the National Natural Science Foundation of China under Grant No.50475109 and No.10572055by the Natural Science Foundation of Gansu Province under Grant No.0803RJZA012
文摘The equations of the asymmetrical periodic motion in a two- -of-freedom vibrating system with two rigid constraints are constructed analytically. Its Poincard mapping equation is established too. Periodic motions of the system and their routes to chaos are also illustrated by numerical simulation. The ranges of the system excited frequency from periodic motions to chaotic motions are obtained. The chaotic motions of the system are shown by di- agrams of Poincarg mapping, phase portraits and diagrams of bifurcation. The chaos controlling methods by the addition of constant load and the addition of phase are dissertated and analyzed numerically by the numerical solu- tion. The chaos of the system is controlled by the two methods. The allowable range controlling variables and the steady orbits of the controlled system are obtained.
