GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW) | ||||||
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21:38 Mar 10, 2004 |
Russian to English translations [PRO] Science - Science (general) / phase trajectories, chaos | |||||||
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| Selected response from: Jack slep Local time: 04:54 | ||||||
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Summary of answers provided | ||||
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4 +1 | period one/two orbit or period one/two limit cycle |
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4 | limit cycle |
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однооборотный предельный цикл limit cycle Explanation: устойчивый предельный цикл - stable limit cycle неустойчивый предельный цикл - unstable limit cycle однооборотный предельный предельный цикл - two stable limit cycles |
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period one/two orbit or period one/two limit cycle Explanation: Varying the control parameter in the logistic map ... This orbit is called a period two orbit (or period two limit cycle), and the two points between which the orbit oscillates are sometimes labelled as period-two ... staff.science.nus.edu.sg/~parwani/c1/node32.html -------------------------------------------------- Note added at 2004-03-11 01:26:35 (GMT) -------------------------------------------------- Numerous examples of phase trajectories, period one, two, etc., orbits can be found in Google, e.g., \"This strange set is generated by an orbit of the bouncing ball system, and it is chaotic in that orbits in this set exhibit sensitive dependence on initial conditions. This sensitive dependence on initial conditions is easy to see in the bouncing ball system when we solve for the impact phases and velocities for the exact model with the numerical procedure described in Appendix A. First consider two slightly different trajectories that converge to the same period one orbit. As shown in Table 1.2, these orbits initially differ in phase by 0.00001. This phase difference increases a little over the next few impacts, but by the eleventh impact the orbits are indistinguishable from each other, and by the eighteenth impact they are indistinguishable from the period one orbit. Thus the difference between the two orbits decreases as the system evolves.\" see above |
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