Dynamic System Modeling Part

To study how landscape features change with the time (i) the spatial part needs landscape feature values only at fairly widely spaced sampling times (communication times) t = t0, 10 + COMINT, 10 + 2*COMINT,...; (2) the communication interval COMINT might be a day, a month, a year, etc.; (3) the dynamic part, however, can increment the time in smaller steps DT to emulate continuous changes. The dynamic part relates the current and future data values at each grid point by ordinary differential equations (we can, instead, relate current and future feature values at different sampling times by difference equations, or by combinations of differential and difference equations):

For each grid point, the feature values q1, q2, ..., the 'state variables', start with given initial values. p1, p2,... are feature values related to the state variables by 'defined-variable assignments'

which must not involve recursive 'algebraic loops'. au a2, ..., b1, b2, ... are fixed parameter values associated with each grid point. The differential equation system [1] for each grid point is solved by numerical integration to produce time histories of the feature values q¡ = q(t) andp¡=p(t). Such an equation system might, for instance, model the growth ofa crop, or the population dynamics of competing plant species at a point ofthe landscape.

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