Identification of Chaotic Dynamics in Jerky-Based Systems by Recurrent Wavelet First-Order Neural Networks with a Morlet Wavelet Activation Function

Autor: Guillermo Huerta Cuellar, Juan Hugo García López, Luis Javier Ontañón García Pimentel, Daniel Alejandro Magallón, Carlos Soubervielle-Montalvo
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Axioms; Volume 12; Issue 2; Pages: 200
ISSN: 2075-1680
DOI: 10.3390/axioms12020200
Popis: Considering that chaotic systems are immersed in multiple areas of science and nature and that their dynamics are governed by a great sensitivity to the initial conditions and variations in their parameters, it is of great interest for the scientific community to have tools to characterize and reproduce these trajectories. Two dynamic chaotic systems whose equations are based on the jerky system are used as benchmarks, i.e., the Memristive Shaking Chaotic System (MSCS) and the Unstable Dissipative System of type I (UDSI). One characteristic common to them is their simple mathematical structure and the complexity of their solutions. Therefore, this paper presents a strategy for identifying chaotic trajectories using a recurrent wavelet first-order neural network (RWFONN) that is trained online with an error filtering algorithm and considering the Morlet-wavelet as an activation function. The parameters of the network are adjusted considering the Euclidean distance between the solutions. Finally, the results depict proper identification of the chaotic systems studied through analysis and numerical simulation to validate the behavior and functionality of the proposed network.
Databáze: OpenAIRE
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