A linear delayed position feedback control is applied to control the erosion of safe basins in a Holmes-Duffing system. The conditions of fractal erosion of the safe basin of the controlled system on the basis that th...A linear delayed position feedback control is applied to control the erosion of safe basins in a Holmes-Duffing system. The conditions of fractal erosion of the safe basin of the controlled system on the basis that the range of time delay leading to good control is obtained by the Melnikov method. It is found that the increasing time delay can reduce the basin erosion under a weak and positive feedback g^in. Then the evolutions of safe basins with time delay are presented in detail by the fourth Runge-Kutta and Monte-Carlo methods, which shows that the safe basin of the controlled Holmes Dulling system can be expanded, and its fractal can be reduced by the increasing time delay. These results suggest that delayed position feedbacks can be used as a good approach to control the erosion of safe basins.展开更多
Fractal erosion of the safe basin in a Helmholtz oscillator system is studied.A linear delayed velocity feedback is employed to suppress the fractal erosion.The necessary basin erosion condition of the delayed feedbac...Fractal erosion of the safe basin in a Helmholtz oscillator system is studied.A linear delayed velocity feedback is employed to suppress the fractal erosion.The necessary basin erosion condition of the delayed feedback controlled system is obtained.The evolution of the boundary and area of the safe basin over time delay is also presented.It follows that the delayed velocity feedback can be used as an effective strategy to control fractal erosion of a safe basin.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 10902071, Shanghai Municipal Education Commission under Grant No YYY08004, Shanghai Leading Academic Discipline Project under Grant No J51501, and Key Project of the National Natural Science Foundation of China under Grant No 11032009
文摘A linear delayed position feedback control is applied to control the erosion of safe basins in a Holmes-Duffing system. The conditions of fractal erosion of the safe basin of the controlled system on the basis that the range of time delay leading to good control is obtained by the Melnikov method. It is found that the increasing time delay can reduce the basin erosion under a weak and positive feedback g^in. Then the evolutions of safe basins with time delay are presented in detail by the fourth Runge-Kutta and Monte-Carlo methods, which shows that the safe basin of the controlled Holmes Dulling system can be expanded, and its fractal can be reduced by the increasing time delay. These results suggest that delayed position feedbacks can be used as a good approach to control the erosion of safe basins.
基金by the Young Scientists Fund of the National Natural Science Foundation of China under Grant No 10902071,“Chen Guang”Project of Shanghai Municipal Education Commission under Grant No 11CG61,Fund of Science and Technology of Shanghai Institute of Technology under Grant No KJ2011-06,the State Key Program of the National Natural Science of China under Grant No 11032009,and Shanghai Leading Academic Discipline Project under Grant No J51501.
文摘Fractal erosion of the safe basin in a Helmholtz oscillator system is studied.A linear delayed velocity feedback is employed to suppress the fractal erosion.The necessary basin erosion condition of the delayed feedback controlled system is obtained.The evolution of the boundary and area of the safe basin over time delay is also presented.It follows that the delayed velocity feedback can be used as an effective strategy to control fractal erosion of a safe basin.
