In this paper, the completed stochastic web and incompleted stochastic web produced by the perturbed saddle separatrix net are given. The structural properties of two kinds of web are discussed by means of the dynamic...In this paper, the completed stochastic web and incompleted stochastic web produced by the perturbed saddle separatrix net are given. The structural properties of two kinds of web are discussed by means of the dynamical system theory.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
A new kind of crisis was observed in a system where a transition from conservative to quasi-dissipative can be observed. The crisis signifies a sudden and intrinsic change of a stochastic web, which is formed by the e...A new kind of crisis was observed in a system where a transition from conservative to quasi-dissipative can be observed. The crisis signifies a sudden and intrinsic change of a stochastic web, which is formed by the end-results of the images of the discontinuous borderlines of the system function. In the crisis, a strange quasi-repeller can be defined. When changing the controlling parameter, the variation of the fractile dimension of the quasi-repeller obeys a logarithmic rule.展开更多
基金The Project supported by the National Natural Science Foundation of China
文摘In this paper, the completed stochastic web and incompleted stochastic web produced by the perturbed saddle separatrix net are given. The structural properties of two kinds of web are discussed by means of the dynamical system theory.
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.
基金The project supported by the National Natural Science Foundation of China (No.10275053)
文摘A new kind of crisis was observed in a system where a transition from conservative to quasi-dissipative can be observed. The crisis signifies a sudden and intrinsic change of a stochastic web, which is formed by the end-results of the images of the discontinuous borderlines of the system function. In the crisis, a strange quasi-repeller can be defined. When changing the controlling parameter, the variation of the fractile dimension of the quasi-repeller obeys a logarithmic rule.
