Change search
Refine search result
1 - 9 of 9
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1. Di Bernardo, M.
    et al.
    Johansson, Karl H.
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Vasca, F.
    Self-oscillations and sliding in relay feedback systems: Symmetry and bifurcations2001In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 11, no 4, p. 1121-1140Article in journal (Refereed)
    Download full text (pdf)
    relay_ijbc01
  • 2. Di Bernardo, M.
    et al.
    Kowalczyk, P.
    Nordmark, Arne B.
    KTH, Superseded Departments, Mechanics.
    Sliding bifurcations: A novel mechanism for the sudden onset of chaos in dry friction oscillators2003In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 13, no 10, p. 2935-2948Article in journal (Refereed)
    Abstract [en]

    Recent investigations of nonsmooth dynamical systems have resulted in the study of a class of novel bifurcations termed as sliding bifurcations. These bifurcations are a characteristic feature of so-called Filippov systems, that is, systems of ordinary differential equations (ODEs) with discontinuous right-hand sides. In this paper we show that sliding bifurcations also play an important role in organizing the dynamics of dry friction oscillators, which are a subclass of nonsmooth systems. After introducing the possible codimension-1 sliding bifurcations of limit cycles, we show that these bifurcations organize different types of slip to stick-slip transitions in dry friction oscillators. In particular, we show both numerically and analytically that a sliding bifurcation is an important mechanism causing the sudden jump to chaos previously unexplained in the literature on friction systems. To analyze such bifurcations we make use of a new analytical method based on the study of appropriate normal form maps describing sliding bifurcations. Also, we explain the circumstances under which the theory of so-called border-collision bifurcations can be used in order to explain the onset of complex behavior in stick-slip systems.

  • 3. Kowalczyk, P.
    et al.
    Di Bernardo, M.
    Champneys, A. R.
    Hogan, S. J.
    Homer, M.
    Piiroinen, P. T.
    Kuznetsov, Yu A.
    Nordmark, Arne B.
    KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics.
    Two-parameter discontinuity-induced bifurcations of limit cycles: Classification and open problems2006In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 16, no 3, p. 601-629Article in journal (Refereed)
    Abstract [en]

    This paper proposes a strategy for the classification of codimension-two discontinuity-induced bifurcations of limit cycles in piecewise smooth systems of ordinary differential equations. Such nonsmooth transitions (also known as C-bifurcations) occur when the cycle interacts with a discontinuity boundary of phase space in a nongeneric way, such as grazing contact. Several such codimension-one events have recently been identified, causing for example, period-adding or sudden onset of chaos. Here, the focus is on codimension-two grazings that are local in the sense that the dynamics can be fully described by an appropriate Poincare map from a neighborhood of the grazing point (or points) of the critical cycle to itself. It is proposed that codimension-two grazing bifurcations can be divided into three distinct types: either the grazing point is degenerate, or the grazing cycle is itself degenerate (e.g. nonhyperbolic) or we have the simultaneous occurrence of two grazing events. A careful distinction is drawn between their occurrence in systems with discontinuous states, discontinuous vector fields, or that with discontinuity in some derivative of the vector field. Examples of each kind of bifurcation are presented, mostly derived from mechanical applications. For each example, where possible, principal bifurcation curves characteristic to the codimension-two scenario are presented and general features of the dynamics discussed. Many avenues for future research are opened.

  • 4.
    Kozlov, Alexander
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Shalfeev, V.D
    Chua, L.O
    Exact synchronization of mismatched chaotic systems1996In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 6, no 3, p. 569-580Article in journal (Refereed)
    Abstract [en]

    In this letter we use adaptive parameter and state feedback control to synchronize two or more slightly mismatched chaotic systems. Chua's circuit with a smooth nonlinearity is used throughout to illustrate our approach. We specify the conditions under which the parameter of a slave system will automatically converge to the parameter of the master system. We also consider potential applications of the control system to problems of secure communications and synchronization of chaos in a chain of slightly different Chua's circuits.

  • 5.
    Kozlov, Alexander
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Sushchik, M.M.
    Molkov, Ya. I.
    Kuznetsov, A.S.
    Bistable phase synchronization and chaos in a system of coupled van der Pol-Duffing oscillators1999In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 9, no 12, p. 2271-2278Article in journal (Refereed)
    Abstract [en]

    Analysis of numerical solutions for a system of two van der Pol-Duffing oscillators with nonlinear coupling showed that there exist chaotic switchings (occurring at irregular time intervals) between two oscillatory regimes differing by nearly time-constant phase shifts between the coupled subsystems. The analysis includes the investigation of bifurcations of the periodic motions corresponding to synchronization of two subsystems, finding stability regions of synchronization regimes and scenarios of the transitions to chaos.

  • 6.
    Möller, Joakim
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Runborg, Olof
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Kevrekidis, P.G.
    Lust, K.
    Kevrekidis, I.G.
    Equation-free, effective computation for discrete systems: a time stepper based approach2005In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 15, no 3, p. 975-996Article in journal (Refereed)
    Abstract [en]

    We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be explicitly constructed. The method only uses a time-integration code for the discrete problem and judicious choices of initial data and integration times; our bifurcation computations are based on the so-called Recursive Projection Method (RPM) with arc-length continuation [Shroff & Keller, 1993]. The technique is used to monitor features of the genuinely discrete problem such as the pinning of coherent structures and its results are compared to quasi-continuum approaches such as the ones based on Pade approximations.

  • 7. Piiroinen, P. T.
    et al.
    Dankowicz, H. J.
    Nordmark, Arne B.
    KTH, Superseded Departments, Mechanics.
    On a normal-form analysis for a class of passive bipedal walkers2001In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 11, no 9, p. 2411-2425Article in journal (Refereed)
    Abstract [en]

    This paper implements a center-manifold technique to arrive at a normal-form for the natural dynamics of a passive, bipedal rigid-body mechanism in the vicinity of infinite foot width and near-symmetric body geometry. In particular, numerical schemes are developed for finding approximate forms of the relevant invariant manifolds and the near-singular dynamics on these manifolds. The normal-form approximations are found to be highly accurate for relatively large foot widths with a range of validity extending to widths on the order of the mechanisms' height.

  • 8. Puig, Julia
    et al.
    Farré, Gerard
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Guillamon, Antoni
    Fontich, Ernest
    Sardanyes, Josep
    Bifurcation Gaps in Asymmetric and High-Dimensional Hypercycles2018In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 28, no 1, article id 1830001Article in journal (Refereed)
    Abstract [en]

    Hypercycles are catalytic systems with cyclic architecture. These systems have been suggested to play a key role in the maintenance and increase of information in prebiotic replicators. It is known that for a large enough number of hypercycle species (n > 4) the coexistence of all hypercycle members is governed by a stable periodic orbit. Previous research has characterized saddle-node (s-n) bifurcations involving abrupt transitions from stable hypercycles to extinction of all hypercycle members, or, alternatively, involving the outcompetition of the hypercycle by so-called mutant sequences or parasites. Recently, the presence of a bifurcation gap between a s-n bifurcation of periodic orbits and a s-n of fixed points has been described for symmetric five-member hypercycles. This gap was found between the value of the replication quality factor Q from which the periodic orbit vanishes (QPO) and the value where two unstable (nonzero) equilibrium points collide (QSS). Here, we explore the persistence of this gap considering asymmetries in replication rates in five-member hypercycles as well as considering symmetric, larger hypercycles. Our results indicate that both the asymmetry in Malthusian replication constants and the increase in hypercycle members enlarge the size of this gap. The implications of this phenomenon are discussed in the context of delayed transitions associated to the so-called saddle remnants.

  • 9.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A recycled characterization of kneading sequences1999In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 9, no 9, p. 1883-1887Article in journal (Refereed)
    Abstract [en]

    For any infinite sequence E on two symbols one can define two sequences of positive integers S(E) (the splitting times) and T(E) (the cosplitting times), which each describe the self-replicative structure of E. If E is the kneading sequence of a unimodal map, it is known that S(E) and T(E) carry a lot of information on the dynamics, and that they are disjoint. We show the reverse implication: A nonperiodic sequence E is the kneading sequence of some unimodal map if the sequences S(E) and T(E) are disjoint.

1 - 9 of 9
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf