by J Awrejcewicz (Inst. of Applied Mechanics, Poland)

This book presents a detailed analysis of bifurcation and chaos in simple non-linear systems, based on previous works of the author. Practical examples for mechanical and biomechanical systems are discussed. The use of both numerical and analytical approaches allows for a deeper insight into non-linear dynamical phenomena. The numerical and analytical techniques presented do not require specific mathematical knowledge.

• Hopf Bifurcation Problem: An Analytical Approach:
  • One Parameter Hopf Bifurcation
  • Biparameter Hopf Bifurcation
  • Bifurcation into Quasiperiodic Torus
  • Hopf Bifurcation in Duffing Oscillator
  • Hopf Bifurcation in Nonstationary Nonlinear Systems
• Bifurcation and Chaos: Numerical Method Based on Solving Boundary Value Problem:
  • Gradual and Sudden Transition to Chaos
  • Three Different Routes to Chaos
  • Bifurcation of the Oscillations of Vocal Cords
• Chaos After Bifurcation of Periodic and Quasiperiodic Orbits:
  • Oscillator with a Static Load and Particular Exciting Force
  • Particular van der Pol — Duffing Oscillator
  • Oscillator with Delay