International Journal of Bifurcation and Chaos · 2002 · 20 citations · 19 references
Natural SciencesPhysicsDifferential EquationsDynamical SystemsPlasma PhysicsBifurcation TheoryChaos TheoryNonlinear DynamicsNonlinear Plasma DynamicsPeriodic OrbitsPlasma StabilityAlfven WavesAlfvén WavesAttractorsChaotic AttractorsChaotic DynamicsNonlinear Schrödinger EquationNumerical Solution Of The Schrödinger EquationUnstable Periodic Orbits
A new transition mechanism to Alfvén chaos via boundary crisis is reported. This crisis appears in a complex plasma region in the presence of a large number of coexisting attractors. We characterize an example of double boundary crises using the unstable periodic orbit determined from the numerical solution of the driven-dissipative derivative nonlinear Schrödinger equation, and demonstrate how the same unstable periodic orbit causes the appearance/disappearance of two chaotic attractors due to two successive homoclinic tangencies.
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Celso Grebogi, Edward Ott, James A. Yorke · Physical Review Letters · 1982 · 792 citations
Critical exponents for crisis-induced intermittency
Celso Grebogi, Edward Ott, F. J. Romeiras et al. · Physical review. A, General physics · 1987 · 564 citations
Nonlinear, dispersive, elliptically polarized Alfvén waves
C. F. Kennel, B. Buti, Tohru Hada et al. · The Physics of Fluids · 1988 · 155 citations