ANALYSIS OF HIDDEN ATTRACTORS OF NON-EQUILIBRIUM FRACTAL-FRACTIONAL CHAOTIC SYSTEM WITH ONE SIGNUM FUNCTION
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Tarih
2022
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
World Scientific Publ Co Pte Ltd
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In 2017, Atangana proposed more generalized operators depending on two parameters: one is fractional order (FO) and other is fractal dimension. The novel operators are defined with three different kernels. These operators produced excellent dynamics of the chaotic systems. In this paper, the Caputo fractal-fractional operator is used to explore a chaotic system which contains only one signum function. The existence theory is developed by using the fixed-point result of Leray-Schauder to prove that the considered chaotic system possesses at least one solution. The proposed chaotic system has a unique solution, according to Banach's fixed-point theorem. We demonstrate that the suggested chaotic system is Ulam-Hyres (UH) stable under the novel operator of power law kernel by employing nonlinear functional analysis. The Adams-Bashforth technique is used to evaluate the numerical outcomes of the considered model. We show the complex structure of numerical solutions for different FO and fractal dimension values.
Açıklama
Anahtar Kelimeler
Signum Function, Chaotic System, Adams-Bashforth Method
Kaynak
Fractals-Complex Geometry Patterns and Scaling in Nature and Society
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
30
Sayı
5
