In this paper, one-state on-off intermittency and two-state on-off intermittency are generated in two five- dimensional continuum systems respectively. In each system, a two-dimensional subsystem is driven by the Ross...In this paper, one-state on-off intermittency and two-state on-off intermittency are generated in two five- dimensional continuum systems respectively. In each system, a two-dimensional subsystem is driven by the Rossler chaotic system. The parameter conditions under which the on-off intermittency occurs are discussed in detail. The statistical property of the intermittency is investigated. It is shown that the distribution of the laminar phase duration time follows a power law with an exponent of -3/2, which is a signature of on-off intermittency. Moreover, the phenomenon of intermingled basins is observed when attractors in the two symmetric invariant subspaces are stable. We provide an effective way to generate on-off intermittency based on a chaotic system, which is important for application and theoretical study.展开更多
A simultaneous change in the systemic property of a kicked billiard ball is observed from an entirely smooth and conservative state to a piecewise smooth and quasi-dissipative state when a single controlling parameter...A simultaneous change in the systemic property of a kicked billiard ball is observed from an entirely smooth and conservative state to a piecewise smooth and quasi-dissipative state when a single controlling parameter has been adjusted. The transition induces a sudden change of a typical conservative stochastic web into a transient web. The iterations on the transient web eventually escape to some elliptic islands. In the meantime, a fat fractal forbidden web, which appears also at the threshold, grows up and cuts away increasingly more parts from the original conservative stochastic web. We numerically show that the initial conditions that generated different attractors are mixed in a random manner and the pattern remains unchanged even when smaller and smaller scales are used for examination, indicating a riddle-like basin structure that practically rules out the possibility of predicting the attractors from a given initial condition.展开更多
文摘In this paper, one-state on-off intermittency and two-state on-off intermittency are generated in two five- dimensional continuum systems respectively. In each system, a two-dimensional subsystem is driven by the Rossler chaotic system. The parameter conditions under which the on-off intermittency occurs are discussed in detail. The statistical property of the intermittency is investigated. It is shown that the distribution of the laminar phase duration time follows a power law with an exponent of -3/2, which is a signature of on-off intermittency. Moreover, the phenomenon of intermingled basins is observed when attractors in the two symmetric invariant subspaces are stable. We provide an effective way to generate on-off intermittency based on a chaotic system, which is important for application and theoretical study.
基金supported by National Natural Science Foundation of China (No. 10275053)
文摘A simultaneous change in the systemic property of a kicked billiard ball is observed from an entirely smooth and conservative state to a piecewise smooth and quasi-dissipative state when a single controlling parameter has been adjusted. The transition induces a sudden change of a typical conservative stochastic web into a transient web. The iterations on the transient web eventually escape to some elliptic islands. In the meantime, a fat fractal forbidden web, which appears also at the threshold, grows up and cuts away increasingly more parts from the original conservative stochastic web. We numerically show that the initial conditions that generated different attractors are mixed in a random manner and the pattern remains unchanged even when smaller and smaller scales are used for examination, indicating a riddle-like basin structure that practically rules out the possibility of predicting the attractors from a given initial condition.
