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" ... However, that water tank over there just seems to defy your linear model fitting: it has a square root relationship of level and flow somewhere. You may try to linearise it around a point, but such a model would be valid in just a narrow interval. And that’s where you make a nonlinear model and observe nonlinear dynamics. It’s fun, it’s exciting and probably hard. You often can’t get an exact solution, but a numerical one, but lo and behold all the rich dynamics you can get from it! The limit cycles, for example. ... "