Reverse engineering of models simulating dynamics of processes occurring in nature is currently an important problem in systems sciences. Model reconstruction is supported by computer-aided inference of the model structure and parameters from measured data and known hypotheses by machine learning and optimization methods. Hypotheses and measured data are often compactly represented by temporal logics.

The goal of this thesis is to propose a technology for reconstruction of the dynamic models representing oscillatory dynamics. The necessary preliminary steps of model reconstruction are: (i) to propose an extension of linear temporal logic allowing expression of oscillatory phenomena, (ii) to propose an algorithm automatically deciding that a model under a given parametrization satisfies a given formula. These steps are solved in this thesis.

The theoretical objectives are the following:

• to select a representative set of non-trivial oscillation properties of dynamic systems,
• to explore possibilities of existing temporal logics in terms of expressing selected oscillatory phenomena,
• to introduce an extension of a suitable temporal logic capable of capturing required properties.

In the practical part, the goal is to design an algorithm that for any given time-series decides validity of any formula of the extended logic. The algorithm will be implemented in terms of prototype Matlab procedures. Finally, evaluation will be provided on several examples and possibly also on a real model case study.