کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
766495 1462609 2016 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Coexistence of multiple attractors and crisis route to chaos in autonomous third order Duffing–Holmes type chaotic oscillators
ترجمه فارسی عنوان
همسویی جذب کننده های متعدد و مسیر بحران به هرج و مرج در حالت سوم خودمختار نوسانگرهای هابز نوع دافینگا هولمز
کلمات کلیدی
نوسانگر دافینگ هولمز سوم شخص مستقل، مدل سازی ریاضی، تقارن بازسازی بحران، جذب چندگانه
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
چکیده انگلیسی

Highlight
• The system is shown to exhibit period-doubling and symmetry restoring crisis routes to chaos.
• It is discovered that the circuit displays four different coexisting attractors.
• Spice simulations results show a very good agreement with the theoretical analysis.

We perform a systematic analysis of a system consisting of an autonomous third order Duffing–Holmes type chaotic oscillator recently introduced by Tamasevicius et al. (2009). In this type of oscillators, the symmetrical characteristics of the nonlinear component necessary for generating chaotic oscillations is synthesized by using a pair of semiconductor diodes connected in anti-parallel. Based on the Shockley diode equation and a judicious choice of state variables, we derive a smooth mathematical model (involving hyperbolic sine and cosine functions) for a better description of both the regular and chaotic dynamics of the oscillator. The bifurcation analysis shows that chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. More interestingly, some regions of the parameter space corresponding to the coexistence of multiple attractors (e.g. coexistence of four different attractors for the same values of system parameters) are discovered. This striking phenomenon is unique and has not yet been reported previously in an electrical circuit (the universal Chua's circuit included, in spite the immense amount of related research work), and thus represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. Some PSpice simulations of the nonlinear dynamics of the oscillator are carried out to verify the theoretical analysis.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 36, July 2016, Pages 29–44
نویسندگان
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