4 edition of **Bifurcations in piecewise-smooth continuous systems** found in the catalog.

- 278 Want to read
- 31 Currently reading

Published
**2010**
by World Scientific in New Jersey
.

Written in English

- Differential equations,
- Bifurcation theory,
- Saccharomyces cerevisiae

Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. Various codimension-two, discontinuity induced bifurcations are unfolded in a rigorous manner. Several of these unfoldings are applied to a mathematical model of the growth of Saccharomyces cerevisiae (a common yeast). The nature of resonance near border-collision bifurcations is described; in particular, the curious geometry of resonance tongues in piecewise-smooth continuous maps is explained in detail. Neimark-Sacker-like border-collision bifurcations are both numerically and theoretically investigated. A comprehensive background section is conveniently provided for those with little or no experience in piecewise-smooth systems.

**Edition Notes**

Statement | David John Warwick Simpson |

Series | World Scientific series on nonlinear science. Series A, Monographs and treatises -- v. 70, World Scientific series on nonlinear science -- v. 70. |

Classifications | |
---|---|

LC Classifications | QA380 .S56 2010 |

The Physical Object | |

Pagination | xv, 238 p. : |

Number of Pages | 238 |

ID Numbers | |

Open Library | OL25085807M |

ISBN 10 | 9814293849 |

ISBN 10 | 9789814293846 |

LC Control Number | 2010484011 |

OCLC/WorldCa | 496957923 |

The study of chaotic systems, either to control or to be used in chaotic regimes, is nowadays of wide interest. These studies are often associated with the analysis of switching systems, leading to piecewise smooth models, either in continuous or in discrete time. An important result, often difficult to get, is the analysis of the regimes in which stable dynamics or chaotic dynamics occur. tions are developed. The class of piecewise smooth systems considered constitutes systems that are smooth everywhere except along borders separating regions of smooth behavior where the system is only continuous. Border collision bifurcations are bifurcations that occur when a ﬁxed point (or a periodic orbit) of a piecewise smooth system crosses.

This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a Price: $ Piecewise Smooth Dynamical Systems Theory: The Case of the Missing Boundary Equilibrium Bifurcations Article (PDF Available) in Journal of Nonlinear Science 26(5) May with Reads.

Continuous planar piecewise linear systems with two linear zones are considered. Due to their low differentiability specific techniques of analysis must be developed. Several bifurcations giving. Lyapunov exponents of piecewise continuous systems of fractional order 3 De nition 4 A set-valued (multi-valued) function F: Rn ⇒ Rn is a function which associates to any element x 2 Rn, a subset of Rn, F(x) (the image of x). There are several ways to de ne F(x).The (convex) de nition was introduced by Filippov in [20] (see also.

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Piecewise-smooth dynamical systems can exhibit most of the bifurcations also exhibited by smooth systems such as period-doublings, saddle-nodes, homoclinic tangencies, etc. provided that these occur away from the discontinuity addition to these, they can also exhibit some novel bifurcation phenomena which are unique to piecewise smooth systems or discontinuity-induced.

Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems.

This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. System Upgrade on Tue, May 19th, at 2am (ET) During this period, E-commerce and registration of new users may not be available for up to 12 hours.

For online purchase, please visit us again. Contact us at [email protected] for any enquiries. Bifurcations in Piecewise-Smooth Continuous Systems Publication: Bifurcations in Piecewise-Smooth Continuous Systems. Edited by SIMPSON DAVID JOHN WARWICK. Published by World Scientific Publishing Co. Pte.

Ltd. Pub Date: DOI: / Bibcode: .S full text sources. Publisher | Cited by: Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and.

Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a surface on which the system is not smooth.

"PSDS presents a valuable compendium of information about the bifurcations of different types of piecewise-smooth systems, but it stops short of completely specifying the mathematical context within which the bifurcation phenomena it discusses are generic.

That leaves lots of interesting work to do in studying piecewise-smooth dynamical systems. This paper deals with the maximum number of limit cycles, which can be bifurcated from periodic orbits of planar piecewise smooth Hamiltonian systems, which are located in a neighborhood of a generalized homoclinic loop with a nilpotent saddle on a switch line.

First we present asymptotic expressions of the Melnikov functions near the loop. We extend a refined version of the subharmonic Melnikov method to piecewise-smooth systems and demonstrate the theory for bi- and trilinear oscillators.

Fundamental results for approximating solutions of piecewise-smooth systems by those of smooth systems are given and used to obtain the main result.

Special attention is paid to degenerate resonance behavior, and analytical results are. This article deals with a two-parameter family of piecewise smooth unimodal maps with one break point. Using superstable cycles and their symbolic representation we describe the structure of the periodicity regions of the 2D bifurcation diagram.

Particular attention is paid to the bistability regions corresponding to two coexisting attractors, and to the border-collision bifurcations. We examine bifurcation phenomena for continuous one-dimensional maps that are piecewise smooth and depend on a parameter μ. In the simplest case, there is a point c at which the map has no.

A theorem regarding planar piecewise-linear continuous systems that gives a condition on the Jacobians under the assumption a limit cycle is created at the discontinuous bifurcation was proved in. Discontinuous bifurcations. Piecewise-smooth, continuous odes may contain bifurcations that do not exist in smooth systems.

Quick Search in Books. Enter words / phrases / DOI / ISBN / keywords / authors / etc. Search. World Scientific Series on Nonlinear Science Series A Bifurcations in Piecewise-Smooth Continuous Systems, pp. i-xv () Free Access. Bifurcations in Piecewise-Smooth Continuous Systems.

Metrics. Downloaded times History. Loading. "Bifurcation and Chaos in Discontinuous and Continuous Systems" provides rigorous mathematical functional-analytical tools for handling chaotic bifurcations along piecewise smooth differential equations, differential and difference inclusions, and differential equations on infinite lattices as well.

This book is intended for mathematicians. These discontinuous piecewise differential systems are formed by two either quadratic, or cubic polynomial differential systems separated by a straight line. We compute the maximum number of limit cycles of these discontinuous piecewise polynomial perturbations of the linear center, which can be obtained by using the averaging theory of order.

Finally, some codimension-two bifurcations of n-dimensional piecewise continuous maps have been studied in, and the results should apply to codimension-two grazing–sliding bifurcations of cycles which, as seen in Sectioninduce a piecewise smooth continuous.

In this paper, we obtain the first-order Melnikov function of piecewise smooth polynomial perturbation of a Hamiltonian system. As application, we consider the number of limit cycles for perturbing the global center and truncated pendulum inside a piecewise smooth cubic polynomial differential system.

Our results show that a piecewise smooth differential system can bifurcate more limit cycles. Quick Search in Books. Enter words / phrases / DOI / ISBN / keywords / authors / etc.

World Scientific Series on Nonlinear Science Series A Bifurcations in Piecewise-Smooth Continuous Systems, pp. () No Access. Fundamentals of Piecewise-Smooth, Continuous Systems Bifurcations in Piecewise-Smooth Continuous Systems. Metrics. Systems of oscillators with piecewise smooth springs and the related grazing bifurcations find applications in many other engineering systems, e.g.

gear pairs, vibrating screens and crushers, vibro-impact absorbers and impact dampers, ships interacting with icebergs (see,), offshore structures (see,), suspension bridges, and.

Such bifurcations are known to occur in piecewise smooth maps, which model many practical and engineering systems. So far the occurrence of such bifurcations. Get this from a library! Bifurcations in piecewise-smooth continuous systems.

[David John Warwick Simpson] -- Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This.In this paper, we consider bifurcations of a class of planar piecewise smooth differential systems constituted by a general linear system and a quadratic Hamiltonian system.

The linear system .Comparing our results with those obtained perturbing the mentioned centers by the continuous quadratic and cubic differential systems we obtain 8 and 9 more limit cycles respectively.