Bifurcations, stability analysis and complex dynamics of Caputo fractal-fractional cancer model

Basit Öğe Kaydı
dc.authoridAhmad, Shabir/0000-0002-5610-6248
dc.authoridUllah, Aman/0000-0003-4021-3599
dc.contributor.authorXuan, Liu
dc.contributor.authorAhmad, Shabir
dc.contributor.authorUllah, Aman
dc.contributor.authorSaifullah, Sayed
dc.contributor.authorAkguel, Ali
dc.contributor.authorQu, Haidong
dc.date.accessioned2024-12-24T19:25:26Z
dc.date.available2024-12-24T19:25:26Z
dc.date.issued2022
dc.departmentSiirt Üniversitesi
dc.description.abstractThe association of cancer and immune cells has complex nature and produces chaotic behavior when it is simulated. The newly introduced operators which combine the fractal and fractional operators produce excellent and profound hidden attractors in a chaotic system which is sometimes not possible to get hidden attractors using integer order operators. The cancer model is considered under fractal fractional operator in Caputo sense. Linear stability of different equilibrium points is analyzed. The primary objective of the current paper is to analyze different bifurcations like pitch-fork, quasi, and inverse period-doubling bifurcations. Another important objective of this article is to study hidden limit cycle type chaotic structures of the cancer model via Caputo fractalfractional operator. The existence and uniqueness of the solution and Ulam-Hyres (UH) stability are studied through the concepts of nonlinear analysis. The numerical solution is derived through the predictor-corrector method. The obtained results were presented and validated through numerical simulations. The lyapunov spectra of the state variables are presented through graphical illustration and table. Sensitivity of the state variables to the initial conditions are simulated for initial conditions 0.1 and 0.11. For various values of fractal dimensions and fractional orders, the time series oscillations and hidden limit cycles type chaotic attractors are graphically presented through MATLAB-17.
dc.description.sponsorshipProject of Guangdong Provincial Depart-ment of Education [2021KTSCX072]
dc.description.sponsorshipThe first author thanks to Project of Guangdong Provincial Depart-ment of Education under NO.2021KTSCX072.
dc.identifier.doi10.1016/j.chaos.2022.112113
dc.identifier.issn0960-0779
dc.identifier.issn1873-2887
dc.identifier.scopus2-s2.0-85129341325
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.chaos.2022.112113
dc.identifier.urihttps://hdl.handle.net/20.500.12604/6416
dc.identifier.volume159
dc.identifier.wosWOS:000802194200001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherPergamon-Elsevier Science Ltd
dc.relation.ispartofChaos Solitons & Fractals
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241222
dc.subjectBifurcations
dc.subjectChaos
dc.subjectFixed point theorems
dc.subjectHidden attractors
dc.subjectFractal dimension
dc.subjectPredictor-corrector method
dc.titleBifurcations, stability analysis and complex dynamics of Caputo fractal-fractional cancer model
dc.typeArticle

Dosyalar

Koleksiyon

WOS İndeksli Yayınlar Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu