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I am trying to find some texts (and/or journal articles) related to the mathematical modeling of transient dynamics. I am a civil engineer and figured physicists/applied mathematicians could tell me where to look. The systems I am looking at are finite dimensional and tend to equilibrate after disruption/disturbance. Equilibrium itself is not of much interest, but the transient part of the process is what I am hoping to look at. Time could be treated in a discrete fashion (the system changes on a day to day basis) or continuously (as an approximation?). I am more interested in stochastic approaches, but also in deterministic.

Transient dynamics are relatively unexplored in my field, so I have to look elsewhere. I've looked at large population (basic diffusion) Gaussian approximations of discrete-time Markov chains, but the ones I found tend to only apply to irreducible MC's (I need transient states). I've looked at some of the unit-root vector time series literature, but the non-stationarity tends to be there throughout the life-time of the process.

Help!