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
In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map op...In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map operations, we give some admissibility conditions for symbolic sequences and find some periodic properties of these symbolic sequences. Then we use these conditions to check the admissibility of periodic symbol sequences.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
With finite computation precision, digital chaos will lose chaotic characteristic. An efficient perturbance-based algorithm perturbing chaos variable algorithm(PCV) was proposed, which can be regarded as a remedy to d...With finite computation precision, digital chaos will lose chaotic characteristic. An efficient perturbance-based algorithm perturbing chaos variable algorithm(PCV) was proposed, which can be regarded as a remedy to digital chaos. After being perturbed, digital chaos systems are able to generate pseudo random sequences with perfect statistical properties and can be used as key stream generators in cryptogram.展开更多
This paper aims at understanding the price dynamics generated by the interaction of traders relying on heterogeneous expectations in an asset pricing model.In the present work the authors analyze a financial market po...This paper aims at understanding the price dynamics generated by the interaction of traders relying on heterogeneous expectations in an asset pricing model.In the present work the authors analyze a financial market populated by five types of boundedly rational speculators-two types of fundamentalists,two types of chartists and trend followers which submit buying/selling orders according to different trading rules.The authors formulate a stock market model represented as a 2 dimensional piecewise linear discontinuous map.The proposed contribution to the existing financial literature is two aspects.First,the authors perform study of the model involving a 2 dimensional piecewise linear discontinuous map through a combination of qualitative and quantitative methods.The authors focus on the existence conditions of chaos and the multi-stability regions in parameter plane.Related border collision bifurcation curves and basins of multi-attractors are also given.The authors find that chaos or quasi-period exists only in the case of fixed point being a saddle(regular or flip)and that the coexistence of multiple attractors may exist when the fixed point is an attractor,but it is common for spiral and flip fixed points.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 National Natural Science Foundation of Chi-na (Grant No .10471087) ,and Shanghai Municipal Commission ofEducation (Grant No .03AK33)
文摘In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map operations, we give some admissibility conditions for symbolic sequences and find some periodic properties of these symbolic sequences. Then we use these conditions to check the admissibility of periodic symbol sequences.
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.
文摘With finite computation precision, digital chaos will lose chaotic characteristic. An efficient perturbance-based algorithm perturbing chaos variable algorithm(PCV) was proposed, which can be regarded as a remedy to digital chaos. After being perturbed, digital chaos systems are able to generate pseudo random sequences with perfect statistical properties and can be used as key stream generators in cryptogram.
基金supported by the Fundamental Research Funds for the Central Universities,South-Central Minzu University under Grant No. CZT20006
文摘This paper aims at understanding the price dynamics generated by the interaction of traders relying on heterogeneous expectations in an asset pricing model.In the present work the authors analyze a financial market populated by five types of boundedly rational speculators-two types of fundamentalists,two types of chartists and trend followers which submit buying/selling orders according to different trading rules.The authors formulate a stock market model represented as a 2 dimensional piecewise linear discontinuous map.The proposed contribution to the existing financial literature is two aspects.First,the authors perform study of the model involving a 2 dimensional piecewise linear discontinuous map through a combination of qualitative and quantitative methods.The authors focus on the existence conditions of chaos and the multi-stability regions in parameter plane.Related border collision bifurcation curves and basins of multi-attractors are also given.The authors find that chaos or quasi-period exists only in the case of fixed point being a saddle(regular or flip)and that the coexistence of multiple attractors may exist when the fixed point is an attractor,but it is common for spiral and flip fixed points.
