A new approach to extreme event prediction and mitigation via Markov-model-based chaos control

Abstract

Despite that the border between chaotic and stochastic systems is exactly defined, scientists, use high dimensional chaotic dynamics to model numerous stochastic models and sometimes use stochastic models to study chaotic systems. In this paper, we have investigated chaotic systems with a stochastic approach and proposed an estimator for the chaotic system which is used to present different algorithms for chaos control, extreme event prediction and extreme event mitigation. The stochastic estimator is constructed by meshing the phase space and applying the cell mapping method (with some considerations) which provides us with a model-free approximation of the systems. The algorithms are ideal for real-world applications where there are some noises and the model of the system is unknown. Besides, the proposed methods are adopted for when the control signal is limited to a few specific values. We have tested these algorithms on Logistic, Henon and a physiological control system.