Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are...Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by dif- ferent mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.展开更多
The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5（P-5） and period-6（P-6） in their coexisting domain of a piecewise linear map are investigated numerically.The probab...The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5（P-5） and period-6（P-6） in their coexisting domain of a piecewise linear map are investigated numerically.The probability densities of some orbits are calculated.When the noise intensity is D = 0.0001,only the orbits of P-5 exist,and the coexisting phenomenon is destroyed.On the other hand,the self-correlation time τ of the colored noise also affects the coexisting phenomenon.When τc〈τ〈τc,only the orbits of P-5 appear,and the stability of the orbits of P-5 is enhanced.However,when τ〉τc（τc and τc are critical values）,only the orbits of P-6 exist,and the stability of the P-6 orbits is enhanced greatly.When τ〈τc,the orbits of P-5 and P-6 coexist,but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.展开更多
The symbolic dynamics of a Belykh-type map （a two-dimensional discon- tinuous piecewise linear map） is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved unde...The symbolic dynamics of a Belykh-type map （a two-dimensional discon- tinuous piecewise linear map） is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved under a hyperbolicity condition. Using this result, a symbolic dynamics model of the map is constructed according to its pruning front and primary pruned region. Moreover, the boundary of the parameter region in which the map is chaotic of a horseshoe type is given.展开更多
A new simple piecewise linear map of the plane is presented and analyzed, then a detailed study of its dynamical behaviour is described, along with some other dynamical phenomena, especially fixed points and their sta...A new simple piecewise linear map of the plane is presented and analyzed, then a detailed study of its dynamical behaviour is described, along with some other dynamical phenomena, especially fixed points and their stability, observation of a new chaotic attractors obtained via border collision bifurcation. An important resuk about coexisting chaotic attractors is also numerically studied and discussed.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No 10275053)
文摘Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by dif- ferent mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10875076)the Science Foundation of the Education Bureau of Shaanxi Province,China (Grant No. 12JK0962)the Science Foundation of Baoji University of Science and Arts of China (Grant No. ZK11053)
文摘The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5（P-5） and period-6（P-6） in their coexisting domain of a piecewise linear map are investigated numerically.The probability densities of some orbits are calculated.When the noise intensity is D = 0.0001,only the orbits of P-5 exist,and the coexisting phenomenon is destroyed.On the other hand,the self-correlation time τ of the colored noise also affects the coexisting phenomenon.When τc〈τ〈τc,only the orbits of P-5 appear,and the stability of the orbits of P-5 is enhanced.However,when τ〉τc（τc and τc are critical values）,only the orbits of P-6 exist,and the stability of the P-6 orbits is enhanced greatly.When τ〈τc,the orbits of P-5 and P-6 coexist,but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.
基金Project supported by the National Natural Science Foundation of China(Nos.11172246 and 11572263)
文摘The symbolic dynamics of a Belykh-type map （a two-dimensional discon- tinuous piecewise linear map） is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved under a hyperbolicity condition. Using this result, a symbolic dynamics model of the map is constructed according to its pruning front and primary pruned region. Moreover, the boundary of the parameter region in which the map is chaotic of a horseshoe type is given.
文摘A new simple piecewise linear map of the plane is presented and analyzed, then a detailed study of its dynamical behaviour is described, along with some other dynamical phenomena, especially fixed points and their stability, observation of a new chaotic attractors obtained via border collision bifurcation. An important resuk about coexisting chaotic attractors is also numerically studied and discussed.
