Chaotic solutions of nonlinear wavewave interacting systems in plasmas
Abstract
The chaotic behavior and phase locking in wavewave interacting systems with linear damping or growth terms are studied. For a two or three wave interaction, the system equations are reducible to a real three dimensional equation on a certain set sigma in the state space. For a three wave interaction, the phases of the waves are locked on sigma. Only systems of positiveenergy waves whose reduced equations may have chaotic behavior for almost all initial conditions are considered. Sufficient conditions for asymptotic phase locking as t approaches infinity are obtained in three wave interacting systems, which depend on the sizes of the attractors for the trajectories. The trajectory behavior of the reduced equations is studied numerically in detail. For certain values of the parameters, the first return mappings of the trajectories have properties which are similar to those of one dimensional mappings having parabolic graphs. Simple models are introduced to explain schematically the transition of attractors for the trajectories. Finally, certain statistical properties of the first return mappings are considered in the light of the known theorems for one dimensional mapping.
 Publication:

Ph.D. Thesis
 Pub Date:
 September 1980
 Bibcode:
 1980PhDT........59M
 Keywords:

 Nonlinear Systems;
 Plasma Waves;
 Wave Interaction;
 Asymptotes;
 Damping;
 Nonequilibrium Conditions;
 Wave Propagation;
 Plasma Physics