Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 1Citation - Scopus: 3Hopf Bifurcations of a Lengyel-Epstein Model Involving Two Discrete Time Delays(Amer inst Mathematical Sciences-aims, 2022) Bilazeroglu, Seyma; Merdan, Huseyin; Guerrini, LucaHopf bifurcations of a Lengyel-Epstein model involving two discrete time delays are investigated. First, stability analysis of the model is given, and then the conditions on parameters at which the system has a Hopf bifurcation are determined. Second, bifurcation analysis is given by taking one of delay parameters as a bifurcation parameter while fixing the other in its stability interval to show the existence of Hopf bifurcations. The normal form theory and the center manifold reduction for functional differential equations have been utilized to determine some properties of the Hopf bifurcation including the direction and stability of bifurcating periodic solution. Finally, numerical simulations are performed to support theoretical results. Analytical results together with numerics present that time delay has a crucial role on the dynamical behavior of Chlorine Dioxide-Iodine-Malonic Acid (CIMA) reaction governed by a system of nonlinear differential equations. Delay causes oscillations in the reaction system. These results are compatible with those observed experimentally.Article Citation - WoS: 11Citation - Scopus: 15Numerical Investigation of Space Fractional Order Diffusion Equation by the Chebyshev Collocation Method of the Fourth Kind and Compact Finite Difference Scheme(Amer inst Mathematical Sciences-aims, 2021) Safdari, Hamid; Azari, Yaqub; Jafari, Hossein; Baleanu, Dumitru; Aghdam, Yones EsmaeelzadeThis paper develops a numerical scheme for finding the approximate solution of space fractional order of the diffusion equation (SFODE). Firstly, the compact finite difference (CFD) with convergence order O(delta tau 2) is used for discretizing time derivative. Afterwards, the spatial fractional derivative is approximated by the Chebyshev collocation method of the fourth kind. Furthermore, time-discrete stability and convergence analysis are presented. Finally, two examples are numerically investigated by the proposed method. The examples illustrate the performance and accuracy of our method compared to existing methods presented in the literature. 1. Introduction. One of the issues which have garnered researchers' attention these days is the fractional differential equations (FDEs) and have been numerically investigated by a huge number of authors [2, 3, 8, 9, 16, 21, 23, 25, 28, 29]. Fractional calculus is involved in many applications of science and engineering such as economics, physics, optimal control, and other applications, see [10, 11, 13, 19, 22, 26, 33, 34, 35]. A case in point is the diffusion and reaction-diffusion models in