Poincare Andronov Melnikov Analysis for Non Smooth Systems 1st Edition by Michal 012804294X 9780128043646

Poincare Andronov Melnikov Analysis for Non Smooth Systems 1st Edition by Michal Feckan – Ebook Instant Download/Delivery ISBN(s): 9780128042946, 012804294X

Product details:

• ISBN 10: 012804294X
• ISBN 13: 9780128043646
• Author: Michal Fečkan

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switching boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions.

Table of contents:

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

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