Order and chaos in nonlinear wave interactions in astrophysical and space plasmas

We discuss the observation and theory of nonlinear wave interactions in astrophysical and space plasmas. Observational evidence of nonlinear mode-mode coupling in solar type III radio bursts, auroral whistler-mode radiation and active experiments in space is reviewed. The transition from order to chaos in nonlinear plasma wave interactions is analysed. For Hamiltonian four-wave interactions, the nonlinear dynamical process may undergo a chaotic transition via the quasi-periodicity route. For dissipative three-wave interactions, the nonlinear system may evolve from order to chaos via two different routes: period doubling and intermittency. It is shown that chaos in dissipative nonlinear three-wave coupling can be controlled by applying a small sinusoidal wave to the system.