Generalized Stability Theory . Part II : Nonautonomous Operators
نویسنده
چکیده
An extension of classical stability theory to address the stability of perturbations to time-dependent systems is described. Nonnonnality is found to play a central role in determining the stability of systems �ovemed by nonautonomous operators associated with time-dependent systems. This pivotal role of nonnonnahty provIdes a conceptual bridge by which the generalized stability theory developed for analysis of autonomous operators can be extended naturally to nonautonomous operators. It has been shown that nonnormality leads to transi�nt growth in autonomous systems, and this result can be extended to show further that time-depende�t non??rmah�y of nonautonomous operators is capable of sustaining this transient growth leading to asymptotIc InstabIhty. ThIS general destabilizing effect associated with the time dependence of the .operator is explored by analyzing para metric instability in periodic and aperiodic time-dependent operators. Simple dynamica� systems are used as examples including the parametrically destabilized harmonic oscillator, growth of errors In the �ore�z system, and the asymptotic destabilization of the quasigeostrophic three-layer model by stochastIc vaCIllatIOn of the zonal wind.
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