物理学报Issue(21)：52-62,11.DOI:10.7498/aps.62.210504
耦合分数阶双稳态振子的同步、反同步与振幅死亡
Synchronization, antisynchronization and amplitude death in coupled fractional order bistable oscillators
摘要
Abstract
The dynamic behaviors of coupled fractional order bistable oscillators are investigated extensively and various phenomena such as synchronization, anti-synchronization, and amplitude death, etc. are explored. Based on the bistable characteristics of P-R oscillator with specific parameters, effects of initial conditions and coupling strength on the dynamic behaviors of the coupled fractional order bistable oscillators are first investigated by analyzing the maximum condition of Lyapunov exponent, the maximum Lyapunov exponent and the bifurcation diagram, etc. Further investigation reveals that the coupled fractional order bistable oscillators can be controlled to form chaotic synchronization, chaotic anti-synchronization, synchronous amplitude death, anti-synchronous amplitude death, partial amplitude death, and so on by changing the initial conditions and the coupling strength. Then, based on the principle of Monte Carlo method, by randomly choosing the initial conditions from the phase space, we calculate the percentage of various states when changing the coupling strength, so the dynamic characteristics of coupled fractional-order bistable oscillators can be represented by using the perspective of statistics. Some representative attractive basins are plotted, which are well coincident with numerical simulations.关键词
振幅死亡/吸引域/双稳态Key words
amplitude death/attractive basin/bistable state引用本文复制引用
王立明,吴峰..耦合分数阶双稳态振子的同步、反同步与振幅死亡[J].物理学报,2013,(21):52-62,11.基金项目
廊坊师范学院基金(批准号:LSZY201204)和国家自然科学青年基金(批准号:11204214)资助的课题.@@@@Project supported by the Langfang Teachers College Foundation, China (Grant No. LSZY201204), and the National Science Fund for Distinguished Young Scholars of China (Grant No.11204214) （批准号:LSZY201204）
