کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5500355 1533978 2017 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Arnold tongues in a billiard problem in nonlinear and nonequilibrium systems
ترجمه فارسی عنوان
زبان آرنولد در یک مسئله بیلیارد در سیستم های غیرخطی و غیرموجب
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی
We study a billiard problem in nonlinear and nonequilibrium systems. This is motivated by the motions of a traveling spot in a reaction-diffusion system (RDS) in a rectangular domain. We consider a four-dimensional dynamical system, defined by ordinary differential equations. This was first derived by S.-I. Ei et al. (2006), based on a reduced system on the center manifold in a neighborhood of a pitchfork bifurcation of a stationary spot for the RDS. In contrast to the classical billiard problem, this defines a dynamical system that is dissipative rather than conservative, and has an attractor. According to previous numerical studies, the attractor of the system changes depending on parameters such as the aspect ratio of the domain. It may be periodic, quasi-periodic, or chaotic. In this paper, we elucidate that it results from parameters crossing Arnold tongues and that the organizing center is a Hopf-Hopf bifurcation of the trivial equilibrium.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 340, 1 February 2017, Pages 14-25
نویسندگان
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