Chaotic (strange) and periodic behavior in instability saturation by the oscillating two‐stream instability
作者:
David A. Russell,
Edward Ott,
期刊:
Physics of Fluids(00319171)
(AIP Available online 1981)
卷期:
Volume 24,
issue 11
页码: 1976-1988
ISSN:0031-9171
年代: 1981
DOI:10.1063/1.863295
出版商: AIP
数据来源: AIP
摘要:
The nonlinear Schro¨dinger equation with linear growth and damping is truncated to three waves. The resulting system of nonlinear ordinary differential equations describes the excitation of linearly damped waves by the oscillating two‐stream instability driven by a linearly unstable pump wave. This system represents a simple model for the nonlinear saturation of a linearly unstable wave. The model is examined analytically and numerically as a function of the dimensionless parameters of the system. It is found that the model can exhibit a wealth of characteristic dynamical behavior including stationary equilibria, Hopf bifurcations to periodic orbits, period doubling bifurcations, chaotic solutions characteristic of a strange attractor, tangent bifurcations from chaotic to periodic solutions, transient chaos, and hysteresis. Many of these features are shown to be explainable on the basis of one‐dimensional maps. In the case of chaotic solutions, evidence for the presence of a strange attractor is provided by demonstrating Cantor set‐like structure (i.e., scale invariance) in the surface of section.
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