Limitations of linear systems
Linear dynamical systems are able to provide a table solutions and to predict some situations of instability. They can take into account the short or medium term changes, but they are not able to provide the whole scope of possible long term changes for instance in environmental complex systems. It is important to observe that linear models enable us to formulate precise predictions about the future of a system, while nonlinear models, in general, only enable such with a degree of approximation which worsens the further into the future we try to predict; essentially, the predictions that nonlinear models provide can, at most, after the event has occurred, tell us why the evolution was of a certain type, why it followed a certain course characterized by particular changes in direction, rather than others, but predictions before the event are more unreliable the larger the intervals of time being considered.
The dynamics of natural systems, just as those of social systems, are not linear; therefore, the more distant the future, the more unpredictable they are. We cannot make long-term predictions, for example, about turbulence that manifests itself not only in the movement of a fluid, but also, for instance, in the financial markets, in the changes of mass opinions and in demographic and macroeconomic developments.
