Abstract:In this paper, we introduce a new chaotic system that is used for an engineering application of the signal encryption. It has some interesting features, and its successful implementation and manufacturing were performed via a real circuit as a random number generator. In addition, we provide a parameter estimation method to extract chaotic model parameters from the real data of the chaotic circuit. The parameter estimation method is based on the attractor distribution modeling in the state space, which is compatible with the chaotic system characteristics. Here, a Gaussian mixture model (GMM) is used as a main part of cost function computations in the parameter estimation method. To optimize the cost function, we also apply two recent efficient optimization methods: WOA (Whale Optimization Algorithm), and MVO (Multi-Verse Optimizer) algorithms. The results show the success of the parameter estimation procedure.
In this paper, we introduce a new chaotic system and its corresponding circuit. This system has a special property of having a hidden attractor. Systems with hidden attractors are newly introduced and barely investigated. Conventional methods for parameter estimation in models of these systems have some limitations caused by sensitivity to initial conditions. We use a geometry-based cost function to overcome those limitations by building a statistical model on the distribution of the real system attractor in state space. This cost function is defined by the use of a likelihood score in a Gaussian Mixture Model (GMM) which is fitted to the observed attractor generated by the real system in state space. Using that learned GMM, a similarity score can be defined by the computed likelihood score of the model time series. The results show the adequacy of the proposed cost function.
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