Asymptotic analysis 1 Asymptotic method 1 Auxiliary function methods 1 Coupled oscillator systems 1 Coupling parameters Damping parameters 1 Higher order statistics 1 Oscillators (mechanical) 1 Parametric oscillators 1 Parametric resonance 1 Region of stabilities 1 Resonance 1 Resonance frequencies 1 Stability regions 1 System stability 1 Time averages 1