You are here

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

Michal Fečkan & Michal Pospíšil
Academic Press
Publication Date: 
Number of Pages: 
We do not plan to review this book.
  • Dedication
  • Acknowledgment
  • Preface
  • About the Authors
  • An introductory example
  • Part I: Piecewise-smooth systems of forced ODEs
    • Introduction
    • Chapter I.1: Periodically forced discontinuous systems
      • I.1.1 Setting of the problem and main results
      • I.1.2 Geometric interpretation of assumed conditions
      • I.1.3 Two-position automatic pilot for ship’s controller with periodic forcing
      • I.1.4 Nonlinear planar applications
      • I.1.5 Piecewise-linear planar application
      • I.1.6 Non-smooth electronic circuits
    • Chapter I.2: Bifurcation from family of periodic orbits in autonomous systems
      • I.2.1 Setting of the problem and main results
      • I.2.2 Geometric interpretation of required assumptions
      • I.2.3 On the hyperbolicity of persisting orbits
      • I.2.4 The particular case of the initial manifold
      • I.2.5 3-dimensional piecewise-linear application
      • I.2.6 Coupled Van der Pol and harmonic oscillators at 1-1 resonance
    • Chapter I.3: Bifurcation from single periodic orbit in autonomous systems
      • I.3.1 Setting of the problem and main results
      • I.3.2 The special case for linear switching manifold
      • I.3.3 Planar application
      • I.3.4 Formulae for the second derivatives
    • Chapter I.4: Sliding solution of periodically perturbed systems
      • I.4.1 Setting of the problem and main results
      • I.4.2 Piecewise-linear application
    • Chapter I.5: Weakly coupled oscillators
      • I.5.1 Setting of the problem
      • I.5.2 Bifurcations from single periodic solutions
      • I.5.3 Bifurcations from families of periodics
      • I.5.4 Examples
    • Reference
  • Part II: Forced hybrid systems
    • Introduction
    • Chapter II.1: Periodically forced impact systems
      • II.1.1 Setting of the problem and main results
    • Chapter II.2: Bifurcation from family of periodic orbits in forced billiards
      • II.2.1 Setting of the problem and main results
      • II.2.2 Application to a billiard in a circle
    • Reference
  • Part III: Continuous approximations of non-smooth systems
    • Introduction
    • Chapter III.1: Transversal periodic orbits
      • III.1.1 Setting of the problem and main result
      • III.1.2 Approximating bifurcation functions
      • III.1.3 Examples
    • Chapter III.2: Sliding periodic orbits
      • III.2.1 Setting of the problem
      • III.2.2 Planar illustrative examples
      • III.2.3 Higher dimensional systems
      • III.2.4 Examples
    • Chapter III.3: Impact periodic orbits
      • III.3.1 Setting of the problem
      • III.3.2 Bifurcation equation
      • III.3.3 Bifurcation from a single periodic solution
      • III.3.4 Poincaré-Andronov-Melnikov function and adjoint system
      • III.3.5 Bifurcation from a manifold of periodic solutions
    • Chapter III.4: Approximation and dynamics
      • III.4.1 Asymptotic properties under approximation
      • III.4.2 Application to pendulum with dry friction
    • Reference
  • Appendix A
    • A.1 Nonlinear functional analysis
    • A.2 Multivalued mappings
    • A.3 Singularly perturbed ODEs
    • A.4 Note on Lyapunov theorem for Hill’s equation
  • Bibliography
  • Index