کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
11031989 1645698 2018 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Numerical patterns in system of integer and non-integer order derivatives
ترجمه فارسی عنوان
الگوهای عددی در سیستم عناصر صحیح و غیر عدد صحیح
موضوعات مرتبط
مهندسی و علوم پایه فیزیک و نجوم فیزیک آماری و غیرخطی
چکیده انگلیسی
This research work contributes to the formation of spatial patterns in fractional-order reaction-diffusion systems. The classical second-order partial derivatives in such systems are replaced with the Riemann-Liouville fractional derivative of order α ∈ (1, 2]. We equally propose a novel numerical scheme for the approximation in space, and the resulting system of equations is advance in time with the improved fourth-order exponential time differencing method. Mathematical analysis of general two-component integer and non-integer order derivatives are provided. To guarantee the correct choice of the parameters in the main dynamics, we carry-out their linear stability analysis. Theorems regarding the local-stability and the conditions for a Hopf-bifurcation to occur are also provided. The proposed numerical method is applied to solve two non-integer-order models, namely the biological (predator-prey) and chemical (activator-inhibitor) systems. We observed some amazing patterns that are completely missing in the classical case at different values of fractional power α in high dimensions that evolve in fractional reaction-diffusion equations.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Chaos, Solitons & Fractals - Volume 115, October 2018, Pages 143-153
نویسندگان
,