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Abstract: The mathematical modeling of the oscillations has attracted considerable attention in recent times, but there is a lack of simple models in the literature that can capture the main features of the dynamics of this important transcription factor. For this reason we propose a simple model that summarizes the key steps of the pathway. We show that the resulting 5-dimensional dynamical system can reproduce different phenomena observed in experiments. Our model can display smooth and spiky oscillations in the amount of nuclear and can reproduce the variety of dynamics observed when different stimulations such as and LPS are used. Furthermore we show that the model can be easily extended to reproduce the expression of early, intermediate and late genes upon stimulation. As a final example we show that our simple model can mimic the different transcriptional outputs observed when cells are treated with two different drugs leading to nuclear localization of : Leptomycin B and Cycloheximide. [Copyright &y& Elsevier]

A well-known method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an in-depth study of this technique. A thorough numerical exploration has been made focused in the important role played by the phase, from which new interesting patterns in parameter space have appeared. On the other hand, our novel experimental implementation of phase control in an electronic circuit confirms both the well-known features of this method and the new ones detected numerically. All this may help in future implementations of phase control of chaos, which is globally confirmed here to be robust and easy to implement experimentally.