Physica D 194 (2004) 275–282 Chaos in driven Alfvén systems: boundary and interior crises Felix A. Borotto a,b,c , Abraham C.-L. Chian b,c,∗ , Tohru Hada c,d , Erico L. Rempel b,c a Departamento de F´ ısica, Universidad de Concepción, Concepción, Chile b National Institute for Space Research (INPE), P.O. Box 515, 12227-010 São José dos Campos-SP, Brazil c World Institute for Space Environment Research (WISER), Brazil d Department of Earth Science and Technology, Kyushu University, Fukuoka 8168580, Japan Received 25 April 2003; accepted 12 February 2004 Communicated by E. Kostelich Abstract Chaotic transitions of nonlinear Alfvén waves via boundary and interior crises are studied. Alfvén crises are characterized using the unstable periodic orbits and their stable and unstable manifolds. In a period-3 periodic window of the bifurcation diagram, we identify a period-9 unstable periodic orbit that is responsible for both boundary and interior crises of two chaotic attractors. We demonstrate that these Alfvén crises arise from a homoclinic tangency. © 2004 Elsevier B.V. All rights reserved. PACS: 05.45.Pq; 52.35.Mw; 52.35.Bj Keywords: Alfvén waves; Plasma; Interior crisis; Boundary crisis; Derivative nonlinear Schrödinger equation 1. Introduction The chaotic behavior of nonlinear Alfvén waves in plasmas is of considerable current interest. Both nondissipative (Hamiltonian) and dissipative Alfvén systems have been studied. For Hamiltonian Alfvén systems, Hada et al. [1] showed that the system dy- namics near the phase-space (soliton) separatrix be- comes chaotic as the driver amplitude increases; Buti [2] investigated the influence of multi-species ions in the degree of chaoticity; Nocera and Buti [3] re- ported the acceleration of chaotic solitons that evolve into an energy-cascade regime exhibiting power-law ∗ Corresponding author. Tel.: +55-12-3945-6956; fax: +55-12-3945-6810. E-mail address: achian@dge.inpe.br (A.C.-L. Chian). URL: http://www.cea.inpe.br/wiser. turbulence spectra in wavenumber and frequency; Buti [4] demonstrated that a small fraction of charged dusty grains can eliminate chaos; de Oliveira et al. [5] identified chaos in a dispersive modulational regime of a coupled system of MHD equations. For dissi- pative Alfvén systems, Ghosh and Papadopoulos [6] showed that as the growth rate of an unstable mode increases, the saturated wave amplitude undergoes period-doubling bifurcations leading to chaos; Hada et al. [1] adopted a three-dimensional dynamical system to analyze the wealth of nonlinear wave dy- namics; Chian et al. [7] proposed a model of Alfvénic intermittent turbulence observed in the solar wind based on the Pomeau-Manneville intermittency and crisis-induced intermittency; Buti et al. [8] showed that inhomogeneities can destroy the integrability of an Alfvén system, inducing chaos even without any 0167-2789/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physd.2004.02.014