Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
4 results
Search Results
Article Citation - WoS: 464Citation - Scopus: 528Discrete Fractional Logistic Map and Its Chaos(Springer, 2014) Baleanu, Dumitru; Wu, Guo-ChengA discrete fractional logistic map is proposed in the left Caputo discrete delta's sense. The new model holds discrete memory. The bifurcation diagrams are given and the chaotic behaviors are numerically illustrated.Article Citation - WoS: 98Citation - Scopus: 121A Nonstandard Finite Difference Scheme for the Modeling and Nonidentical Synchronization of a Novel Fractional Chaotic System(Springer, 2021) Baleanu, D.; Zibaei, S.; Namjoo, M.; Jajarmi, A.The aim of this paper is to introduce and analyze a novel fractional chaotic system including quadratic and cubic nonlinearities. We take into account the Caputo derivative for the fractional model and study the stability of the equilibrium points by the fractional Routh–Hurwitz criteria. We also utilize an efficient nonstandard finite difference (NSFD) scheme to implement the new model and investigate its chaotic behavior in both time-domain and phase-plane. According to the obtained results, we find that the new model portrays both chaotic and nonchaotic behaviors for different values of the fractional order, so that the lowest order in which the system remains chaotic is found via the numerical simulations. Afterward, a nonidentical synchronization is applied between the presented model and the fractional Volta equations using an active control technique. The numerical simulations of the master, the slave, and the error dynamics using the NSFD scheme are plotted showing that the synchronization is achieved properly, an outcome which confirms the effectiveness of the proposed active control strategy. © 2021, The Author(s).Article Citation - WoS: 37Citation - Scopus: 63Chaotic Incommensurate Fractional Order Rossler System: Active Control and Synchronization(Springer, 2011) Majd, Vahid Johari; Baleanu, Dumitru; Razminia, AbolhassanIn this article, we present an active control methodology for controlling the chaotic behavior of a fractional order version of Rossler system. The main feature of the designed controller is its simplicity for practical implementation. Although in controlling such complex system several inputs are used in general to actuate the states, in the proposed design, all states of the system are controlled via one input. Active synchronization of two chaotic fractional order Rossler systems is also investigated via a feedback linearization method. In both control and synchronization, numerical simulations show the efficiency of the proposed methods.Article Citation - WoS: 146Citation - Scopus: 163Discrete Chaos in Fractional Delayed Logistic Maps(Springer, 2015) Baleanu, Dumitru; Wu, Guo-ChengRecently the discrete fractional calculus (DFC) started to gain much importance due to its applications to the mathematical modeling of realworld phenomena with memory effect. In this paper, the delayed logistic equation is discretized by utilizing the DFC approach and the related discrete chaos is reported. The Lyapunov exponent together with the discrete attractors and the bifurcation diagrams are given.