Canards in Complex Oscillatory Systems

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Naghdabadi, Zahra | 2021

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 54120 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Razvan, Mohammad Reza
Abstract:
Canard, first observed in Van der Pol oscillations, is a typical phenomenon in oscillatory systems. Canard is also observed in many oscillatory systems such as electrical circuits and neurons. In many fields of science and engineering there are complex oscillations that exhibit canard for certain values of parameters. These three dimensional systems exhibit complex oscillatory behavior never observed in two dimensional dynamics. Some of these systems are chaotic for certain parameter values. It seems than in oscillatory systems canards can make complex behavior. Several methods such as the singular perturbation theory have been used to study this complexity. In this project, we study canard and its role in changing dynamics of oscillatory systems with complex behavior
Keywords:
Chaos Dynamics ; Canard ; Complex Oscillatory Behavior ; Oscillatory System

مفاهیم اولیه
- سیستم‌های تند-کند و نظیریه هندسی اغتشاش تکین
مقدمه ای از کانارد
- قضایای فنیشل
  - تکینگی‌های تاخورده و کانارد تکین
- انواع کانارد
آنالیز کانارد
- کانارد در بعد دو
  - آنالیز کانارد در یک نقطه
- کانارد در بعد سه
  - گره زینی تاخورده
  - گره های تاخورده تباهیده
کانارد در سیستم‌های دینامیکی
- کانارد و نوسانات وندرپل
- کانارد و سیستم فیتزهیو-ناگومو
کانارد و دینامیک سرتاسری
چکیده انگلیسی