1 edition of **Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles** found in the catalog.

- 227 Want to read
- 32 Currently reading

Published
**2012**
by Springer London in London
.

Written in English

- Differential equations,
- Differentiable dynamical systems,
- Approximations and Expansions,
- Dynamical Systems and Ergodic Theory,
- Ordinary Differential Equations,
- Mathematical Software,
- Nonlinear Dynamics,
- Mathematics,
- Computer software

**Edition Notes**

Statement | by Maoan Han, Pei Yu |

Series | Applied Mathematical Sciences -- 181 |

Contributions | Yu, Pei, SpringerLink (Online service) |

The Physical Object | |
---|---|

Format | [electronic resource] / |

ID Numbers | |

Open Library | OL27077746M |

ISBN 10 | 9781447129189 |

Based on the first three Melnikov functions M 1 (h), M 2 (h) and M 3 (h), three limit cycles has been obtained. Choosing a different decomposition for our system, we will show below that one can use the Melnikov functions M k (h) of any order k ≥ 1 in studying the limit cycles. A maximum number of three limit cycles is obtained for the system. This book introduces the recent developments in the field and provides major advances in fundamental theory of limit cycles. It considers near Hamiltonian systems using Melnikov function as the main mathematical d Mathematical Sciences: Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles (Paperback)Brand: Maoan Han; Pei Yu.

We use two methods, the Melnikov function method and the method of stability-changing of a homoclinic loop or a double homoclinic loop to study this problem. We find 15 limit cycles and 16 limit cycles respectively with four alien limit cycles under certain conditions. Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles by Maoan Han & Pei Yu Author:Maoan Han & Pei Yu, Date: April 5, ,Views:

Bifurcation of limit cycles via Melnikov function where {Pj} are analytic functions with Pj(0,0,δ) = 0,j = 1,, implies from the above form of F that F has at most k−1 positive zeros in , k−1 positive zeros can appear. The condition () means that the origin is always a singular point under per-. For the conservative system, two main results were obtained, Theorems 1 and 2, where we establish analytically the bifurcation diagram of the equilibria for specific regions with the involved parameters in contrast to the one obtained in [].In particular, Theorem 2 proves the local existence of two saddle-node bifurcations that can be related to the hysteresis phenomenon [17, 18].

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This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near.

Buy Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles (Applied Mathematical Sciences, Vol. ) (Applied Mathematical Sciences ()) on FREE SHIPPING on qualified ordersCited by: Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles.

Authors: Han, Maoan, Yu, Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for.

This book introduces the most recent developments in this field and provides advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near.

Normal forms, Melnikov functions and bifurcations of limit cycles Maoan Han, Pei Yu (auth.) Dynamical system theory has developed rapidly over the past fifty years.

It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems.

Request PDF | Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles | Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of. Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles.

por Maoan Han,Pei Yu. Applied Mathematical Sciences (Book ) ¡Gracias por compartir. Has enviado la siguiente calificación y reseña. Lo publicaremos en nuestro sitio después de haberla : Springer London.

Han / Yu, Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles,Buch, Bücher schnell und portofrei. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles.

Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert's 16th problem, while the second considers near.

Han M., Yu P. () Fundamental Theory of the Melnikov Function Method. In: Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles. Applied Mathematical Sciences, vol Normal forms, Melnikov functions and bifurcations of limit cycles Subject: London, Springer, Keywords: Signatur des Originals (Print): RA ().

Digitalisiert von der TIB, Hannover, Created Date: 8/28/ PM. Han M., Yu P. () Finding More Limit Cycles Using Melnikov Functions. In: Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles.

Applied Mathematical Sciences, vol Introduction --Hopf bifurcation and normal form computation --Comparison of methods for computing focus values --Application (I): Hilbert's 16th problem --Application (II): practical problems --Fundamental theory of the Melnikov function method --Limit cycle bifurcations near a center --Limit cycles near a homoclinic or heteroclinic loop.

from book Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles (pp) Fundamental Theory of the Melnikov Function Method Chapter January with 13 Reads. In this paper we focus on the combination of normal form and Lyapunov exponent computations in the numerical study of the three codim 2 bifurcations of limit cycles with dimension of the center manifold equal to 4 or to 5 in generic autonomous ODEs.

The normal form formulas are independent of the dimension of the phase space and involve solutions of certain linear boundary.

Explicit computational formulas for the coefficients of the normal forms for all codim 2 equilibrium bifurcations of equilibria in autonomous ODEs are derived. Analysis of bifurcations of limit cycles with Lyapunov exponents and numerical normal forms. Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles, Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles, () Practical computation of normal forms of the Bogdanov–Takens bifurcation.

Nonlinear Dynamics The function M plays an important role in the study of limit cycles, and has been studied by many mathematicians (see e.g. [1â€“12]). In the study of Hopf bifurcation for system (), a general assumption widely used is that the origin is an elementary singular point (see e.g.

[4â€“ 10,13]). Han, M. & Yu, P. [ ] Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles (Springer-Verlag, London). Crossref, Google Scholar Han, M., Yang, J. & Xiao, D. [ ] “ Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle,” Int.

Bifurcation and Ch – Read "Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles" by Maoan Han available from Rakuten Kobo.

Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit Brand: Springer London. Hopf bifurcation is studied to show complex dynamics due to multiple limit cycles bifurcation.

In particular, normal form theory is applied to prove that three limit cycles can bifurcate from an equilibrium in the vicinity of a Hopf critical point, yielding a new bistable phenomenon which involves two stable limit cycles.This thesis contains two parts. In the first part, we investigate bifurcation of limit cycles around a singular point in planar cubic systems and quadratic switching systems.

For planar cubic systems, we study cubic perturbations of a quadratic Hamiltonian system and obtain 10 small-amplitude limit cycles bifurcating from an elementary center, for which up to 5th-order Melnikov functions are used.

Limit cycle bifurcations near a generalized homoclinic loop in piecewise smooth systems P. YuNormal Forms, Melnikov Functions and Bifurcations of Limit Cycles.

Springer-Verlag, London () by the Natural Science Foundation of Anhui Province (No: MA08), Doctor Program Foundation () of Anhui Normal University, the NSF of.