Toward analytical chaos in nonlinear systems /

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"Exact analytical solutions to periodic motions in nonlinear dynamical systems are almost not possible. Since the 18th century, one has extensively used techniques such as perturbation methods to obtain approximate analytical solutions of periodic motions in nonlinear systems. However, the pert...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Luo, Albert C. J.
Format: Electronic eBook
Language:Inglés
Published: Chichester, West Sussex, United Kingdom : Wiley, 2014.
Subjects:
Differentiable dynamical systems.
Nonlinear oscillations.
Chaotic behavior in systems.
Dynamique différentiable.
Oscillations non linéaires.
Chaos.
TECHNOLOGY & ENGINEERING > Mechanical.
Chaotic behavior in systems
Differentiable dynamical systems
Nonlinear oscillations
Online Access:Texto completo (Requiere registro previo con correo institucional)
Table of Contents:
  • Machine generated contents note: 1. Introduction
  • 1.1. Brief History
  • 1.2. Book Layout
  • 2. Nonlinear Dynamical Systems
  • 2.1. Continuous Systems
  • 2.2. Equilibriums and Stability
  • 2.3. Bifurcation and Stability Switching
  • 2.3.1. Stability and Switching
  • 2.3.2. Bifurcations
  • 3. Analytical Method for Periodic Flows
  • 3.1. Nonlinear Dynamical Systems
  • 3.1.1. Autonomous Nonlinear Systems
  • 3.1.2. Non-Autonomous Nonlinear Systems
  • 3.2. Nonlinear Vibration Systems
  • 3.2.1. Free Vibration Systems
  • 3.2.2. Periodically Excited Vibration Systems
  • 3.3. Time-Delayed Nonlinear Systems
  • 3.3.1. Autonomous Time-Delayed Nonlinear Systems
  • 3.3.2. Non-Autonomous Time-Delayed Nonlinear Systems
  • 3.4. Time-Delayed, Nonlinear Vibration Systems
  • 3.4.1. Time-Delayed, Free Vibration Systems
  • 3.4.2. Periodically Excited Vibration Systems with Time-Delay
  • 4. Analytical Periodic to Quasi-Periodic Flows
  • 4.1. Nonlinear Dynamical Systems
  • 4.2. Nonlinear Vibration Systems
  • 4.3. Time-Delayed Nonlinear Systems
  • 4.4. Time-Delayed, Nonlinear Vibration Systems
  • 5. Quadratic Nonlinear Oscillators
  • 5.1. Period-1 Motions
  • 5.1.1. Analytical Solutions
  • 5.1.2. Frequency-Amplitude Characteristics
  • 5.1.3. Numerical Illustrations
  • 5.2. Period-m Motions
  • 5.2.1. Analytical Solutions
  • 5.2.2. Analytical Bifurcation Trees
  • 5.2.3. Numerical Illustrations
  • 5.3. Arbitrary Periodical Forcing
  • 6. Time-Delayed Nonlinear Oscillators
  • 6.1. Analytical Solutions
  • 6.2. Analytical Bifurcation Trees
  • 6.3. Illustrations of Periodic Motions.

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