Forecasting and Chaos

  • Juan C. Vallejo
  • Miguel A. F. Sanjuan
Part of the Springer Series in Synergetics book series (SSSYN)


Forecasting is the process of making predictions of the future based on past and present data. One of the key questions of the scientific method is the possibility of making predictions using a model and to confront them with new observations as a test of its goodness. It seems rather natural to think that with an adequate increase in numerical computational facilities, the errors could be neglected and that from a set of initial conditions which are known with enough precision, one could predict the future state of a dynamical system. However, every model has inherent inaccuracies leading its results to deviate from the true solution. Furthermore, the computational issues constitute another source of errors. When a system shows a strong sensitivity to the initial conditions, then the system is chaotic. And when the nonlinearity is present, one prediction can be destroyed by an initial error, even by a very small one. Fortunately, the presence of chaos does not always imply a low predictability. An orbit can be chaotic and still be predictable, in the sense that the chaotic orbit is followed, or shadowed, by a real orbit, thus making its predictions physically valid.


Lyapunov Exponent Chaotic System Kutta Method Chaotic Orbit Regular Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer International Publishing AG 2017

Authors and Affiliations

  • Juan C. Vallejo
    • 1
  • Miguel A. F. Sanjuan
    • 1
  1. 1.Department of PhysicsUniversidad Rey Juan CarlosMóstoles, MadridSpain

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