کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
7374810 1480064 2018 44 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Discrete chaotic maps obtained by symmetric integration
ترجمه فارسی عنوان
نقشه های هرج و مرج گسسته به دست آمده از یکپارچگی متقارن
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
چکیده انگلیسی
Chaotic return maps are widely used to model various dynamical systems such as charged particle movement, laser beam dynamic, celestial body orbiting and many others. Return maps are commonly obtained by discretization of continuous equations using the Euler-Cromer operator with the only motivation that it is the simplest symplectic operator. Recent progress in geometric integration raised considerable interest to symmetric operators due to their ability to preserve some geometric properties of continuous flows this way yielding better agreement between discrete and continuous dynamical systems. Here we compare symmetric and asymmetric discretization approaches applied to several examples of Hamiltonian systems. In particular, we suggest symmetric modifications of Chirikov and Hénon maps and show explicitly that the implied symmetric integration procedure yields reflectional symmetry in the phase space. For verification, we show that a smooth even perturbation function used instead of a discontinuous delta pulse provides asymptotically similar results. Numerical experiments using several statistical methods show that symmetric and asymmetric maps, while yielding similar asymptotic behavior, often exhibit considerably different statistical properties for intermediate regimes providing smoother transitions that are more reminiscent to those observed in various natural phenomena. We believe that the proposed approach may be useful for modeling empirical systems by preserving their keynote physical properties.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica A: Statistical Mechanics and its Applications - Volume 509, 1 November 2018, Pages 955-970
نویسندگان
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