abstract

• 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.

authors

• Ontañón García Pimentel Luis Javier
• Soubervielle Montalvo Carlos

publication date

• 2023-01-01

funding provided via

• CONACyT [2290436. G.H.C.]; Consejo Estatal de Tecnología de Jalisco (COECYTJAL) [10304-2022]  Grant

published in

• Axioms   Journal

keywords

• dynamic systems, chaos theory, artificial neural network, error filter algorithm, Morlet-wavelet activation function

Digital Object Identifier (DOI)

• 10.3390/axioms12020200

PubMed ID

start page

• 1

end page

• 13

volume

• 12

issue

• 2