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Considering a class of complex nonlinear systems whose dynamics are mostly governed by statistical regulations, the pattern-moving theory was developed to characterise such systems and successfully estimate the outputs or states. However, since the pattern class variable is not computable directly, this study establishes a clustered generalized cell mapping (C-GCM) to reveal system characteristics. C-GCM is a two-stage approach consisting of a pattern-moving-based description and analysis method. First, a density algorithm, named density-based spatial clustering of applications with noise (DBSCAN), is designed to obtain cell space Ω and the corresponding classification guidelines; this algorithm is initiated after the initial pre-image cells, and the total number of entity cells amounts to Ns. Then, the GCM provides several image cells based on a cell mapping function that refers to the multivariate ARMAX model. The global dynamic analysis employing both searching and storing algorithms depend on the attractor, domain of attraction, and periodic cell groups. At last, simulation results of two examples emphasise the practicality as well as efficacy of the technique suggested. The chief aim of this study was to offer a new perspective for a class of complex systems that could inspire research into nonmechanistic principles modelling and application to nonlinear systems.
Li et al. (2024) studied this question.