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Sunday, November 15, 2020 | History

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

Bifurcations in piecewise-smooth continuous systems

  • 38 Want to read
  • 39 Currently reading

Published by World Scientific in New Jersey .
Written in English

    Subjects:
  • Differential equations,
  • Bifurcation theory,
  • Saccharomyces cerevisiae

  • About the Edition

    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

    StatementDavid John Warwick Simpson
    SeriesWorld Scientific series on nonlinear science. Series A, Monographs and treatises -- v. 70, World Scientific series on nonlinear science -- v. 70.
    Classifications
    LC ClassificationsQA380 .S56 2010
    The Physical Object
    Paginationxv, 238 p. :
    Number of Pages238
    ID Numbers
    Open LibraryOL25085807M
    ISBN 109814293849
    ISBN 109789814293846
    LC Control Number2010484011
    OCLC/WorldCa496957923


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Bifurcations in piecewise-smooth continuous systems by David John Warwick Simpson Download PDF EPUB FB2

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 Bifurcations in piecewise-smooth continuous systems book 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.

A review is presented of the one-parameter, nonsmooth bifurcations that occur in a variety of continuous-time piecewise-smooth dynamical systems. Motivated by applications, a pragmatic approach is taken to defining a discontinuity-induced bifurcation (DIB) as a nontrivial interaction of a limit set with respect to a codimension-one.

() Torus destruction via global bifurcations in a piecewise-smooth, continuous map with square-root nonlinearity. Physics Letters A() Simultaneous border-collision and period-doubling bifurcations. 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. 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.

Much of our understanding of these cases relies on a reduction to piecewise linearity near the border collision. cycles which bifurcate from a weak focus for piecewise smooth continuous systems.

Bifurcation of limit cycles by perturbing piecewise smooth Hamiltonian systems has been studied in [17,18,24]. Generally speaking, piecewise smooth di erential system can. Get this from a library. Continuous and discontinuous piecewise-smooth one-dimensional maps: invariant sets and bifurcation structures.

[Viktor Avrutin; L Gardini; Irina Sushko; Fabio Tramontana] -- "Although the dynamic behavior of piecewise-smooth systems is still far from being understood completely, some significant results in this field have been achieved in the last twenty years.

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems D.J.W. Simpsona,1, J.D. Meissb,2, aDepartment of Mathematics, University of British Columbia, Vancouver, BC, V6T1Z2, Canada bDepartment of Applied Mathematics, University of Colorado, Boulder, CO,USA Abstract Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems.

Get this from a library. Bifurcations and chaos in piecewise-smooth dynamical systems. [Zhanybai T Zhusubaliyev; Erik Mosekilde] -- "Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they.

This Letter outlines 20 geometric mechanisms by which limit cycles are created locally in two-dimensional piecewise-smooth systems of ODEs. These include boundary equilibrium bifurcations of hybrid systems, Filippov systems, and continuous systems, and limit cycles created from folds and by the addition of hysteresis or time-delay.

In each case a stationary solution, such as a regular. 2Department of Systems and Computer Engineering, University of Naples, Federico II, Italy This paper presents an overview of the current state of the art in the analysis of discontinuity-induced bifurcations (DIBs) of piecewise smooth dynamical systems, a particularly relevant class of hybrid dynamical systems.

Firstly, we present a classification. Feedback control of border collision bifurcations in continuous piecewise smooth discrete-time systems is considered.

These bifurcations occur when a fixed point or a periodic orbit of a piecewise smooth system crosses or collides with the border between two regions of smooth operation as a system parameter is quasistatically varied. In recent years the theory of border collision bifurcations has been developed for piecewise smooth maps that are continuous across the border, and has been success-fully applied to explain nonsmooth bifurcation phenomena in physical systems.

How-ever, many switching dynamical systems have been found to yield two-dimensional. This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems.piecewise-smooth systems based on their dependence on time.

The piecewise-smooth systems having a continuous time dependence are further classi ed as Filippov systems or Flows based on the order of their discontinuity. Filippov systems have a discontinuity of .