Emotional Chaotic Cuckoo Search for the Reconstruction of Chaotic Dynamics

Among most machine learning algorithms for optimization problem including meta-heuristic search algorithms, the solution is drawn like a moth to a flame and cannot keep away. The track of chaotic variable can travel ergodically over the whole search space. In general, the chaotic variable has special characters, i.e., ergodicity, pseudo-randomness and irregularity. To enrich the searching behavior and to avoid being trapped into local optimum, chaotic dynamics is incorporated into the proposed emotional chaotic cuckoo search algorithm. Firstly, a chaotic Levy flight is introduced in the proposed meta-heuristic search for efficiently generating new solutions. Secondly, psychology model of emotion and chaotic sequence is proposed for move acceptance decision in cuckoo search algorithm. The rich nonlinear dynamics of chaos allows to model a broad variety of systems, including complex biological ones. The system of interest is usually observed through some time series and the modeling problem consists of adjusting the parameters of a model chaotic system until its dynamics is matched to the reference time series. In this way, the secondary parameters are interpreted as estimates of the primary ones. In this paper, we describe a general methodology to adaptively select the values of the model parameters for the reconstruction of chaotic dynamics. A new approach to cuckoo search optimization is developed. We illustrate the application of the method by jointly estimating the complete parameter vector of a Lorenz system. Key-Words: chaotic dynamics, psychology model of emotion, cuckoo search, chaotic sequence