Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary,...Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary,spiral waves and spatiotemporal chaos can be eliminated by the trains for some certain excitation periods. Obvious resonant behavior can be observed from the relation between the periods of the trains and excitation ones. The method is against noise.展开更多
The influence of a soliton system under an external harmonic excitation is considered. We take the compound KdV-Burgers equation as an example, and investigate numerically the chaotic behavior of the system with a per...The influence of a soliton system under an external harmonic excitation is considered. We take the compound KdV-Burgers equation as an example, and investigate numerically the chaotic behavior of the system with a periodic forcing. Different routes to chaos such as period doubling, quasi-periodic routes, and the shapes of strange attractors are observed by using bifurcation diagrams, the largest Lyapunov exponents, phase projections and Poincaré maps.展开更多
In this paper,the complicated dynamics and multi-pulse homoclinic orbits of a two-degree-of-freedom parametrically excited nonlinear nano-oscillator with coupled cubic nonlinearities are studied.The damping,parametric...In this paper,the complicated dynamics and multi-pulse homoclinic orbits of a two-degree-of-freedom parametrically excited nonlinear nano-oscillator with coupled cubic nonlinearities are studied.The damping,parametrical excitation and the nonlinearities are regarded as weak.The averaged equation depicting the fast and slow dynamics is derived through the method of multiple scales.The dynamics near the resonance band is revealed by doing a singular perturbation analysis and combining the extended Melnikov method.We are able to determine the criterion for the existence of the multi-pulse homoclinic orbits which can form the Shilnikov orbits and give rise to chaos.At last,numerical results are also given to illustrate the nonlinear behaviors and chaotic motions in the nonlinear nano-oscillator.展开更多
基金国家重点基础研究发展计划(973计划)，中国科学院资助项目，国家自然科学基金，the Innovation Funds for Laser Technology，the Science Foundation of the Chinese Academy of Engineering Physics
文摘Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary,spiral waves and spatiotemporal chaos can be eliminated by the trains for some certain excitation periods. Obvious resonant behavior can be observed from the relation between the periods of the trains and excitation ones. The method is against noise.
基金＊The project supported by the Natural Science Foundation of Zhejiang Province of China under Grant No. 101003 and the Foundation of ＂151 Talent Engineering＂ of Zhejiang Province of China. 0ne of the authors （Yu） would like to thank Dr. Ze-Yuan Huang, Profs. Sen-Yue Lou and Min Qian for their helpful discussions.
文摘The influence of a soliton system under an external harmonic excitation is considered. We take the compound KdV-Burgers equation as an example, and investigate numerically the chaotic behavior of the system with a periodic forcing. Different routes to chaos such as period doubling, quasi-periodic routes, and the shapes of strange attractors are observed by using bifurcation diagrams, the largest Lyapunov exponents, phase projections and Poincaré maps.
基金supported by the National Natural Science Foundation of China(Grant Nos.11290152,11072008 and 11372015)the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality(PHRIHLB)
文摘In this paper,the complicated dynamics and multi-pulse homoclinic orbits of a two-degree-of-freedom parametrically excited nonlinear nano-oscillator with coupled cubic nonlinearities are studied.The damping,parametrical excitation and the nonlinearities are regarded as weak.The averaged equation depicting the fast and slow dynamics is derived through the method of multiple scales.The dynamics near the resonance band is revealed by doing a singular perturbation analysis and combining the extended Melnikov method.We are able to determine the criterion for the existence of the multi-pulse homoclinic orbits which can form the Shilnikov orbits and give rise to chaos.At last,numerical results are also given to illustrate the nonlinear behaviors and chaotic motions in the nonlinear nano-oscillator.
