SlideCont: An Auto97 driver for bifurcation analysis of Filippov systems

被引：79
作者：
Dercole, F
Kuznetsov, YA
机构：
[1] Politecn Milan, Dept Elect & Informat, I-20133 Milan, Italy
[2] Univ Utrecht, Dept Math, NL-3508 TC Utrecht, Netherlands
[3] Russian Acad Sci, Inst Math Problems Biol, Pushchino 142290, Moscow Region, Russia
来源：
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE | 2005年 / 31卷 / 01期
关键词：
algorithms; AuTo97; numerical continuation; piecewise-smooth differential equations; Filippov systems; sliding bifurcations;
D O I：
10.1145/1055531.1055536
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
SLIDECONT, an AUTO97 driver for sliding bifurcation analysis of discontinuous piecewise-smooth autonomous systems, known as Filippov systems, is described in detail. Sliding bifurcations are those in which some sliding on the discontinuity boundary is critically involved. The software allows for detection and continuation of codimension-1 sliding bifurcations as well as detection of some codimension-2 singularities, with special attention to planar systems (n = 2). Some bifurcations are also supported for n-dimensional systems. This article gives a brief introduction to Filippov systems, describes the structure Of SLIDECONT and all computations supported by SLIDECONT 2.0. Several examples, which are distributed together with the source code Of SLIDECONT, are presented.
引用
收藏
页码：95 / 119
页数：25
相关论文
共 18 条
  • [1] [Anonymous], 1997, AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations, user's Manual
  • [2] [Anonymous], 1994, FORCED OSCILLATIONS
  • [3] COLLOCATION SOFTWARE FOR BOUNDARY-VALUE DIFFERENTIAL-ALGEBRAIC EQUATIONS
    ASCHER, UM
    SPITERI, RJ
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1994, 15 (04) : 938 - 952
  • [4] Numerical sliding bifurcation analysis: An application to a relay control system
    Dercole, F
    Gragnani, A
    Kuznetsov, YA
    Rinaldi, S
    [J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2003, 50 (08) : 1058 - 1063
  • [5] DERCOLE F, 2004, USER GUIDE SLIDECONT
  • [6] DERCOLE F, 2002, 1261 UTR U DEP MATH
  • [7] Local analysis of C-bifurcations in n-dimensional piecewise-smooth dynamical systems
    Di Bernardo, M
    Feigin, MI
    Hogan, SJ
    Homer, ME
    [J]. CHAOS SOLITONS & FRACTALS, 1999, 10 (11) : 1881 - 1908
  • [8] di Bernardo M, 1998, NONLINEARITY, V11, P859, DOI 10.1088/0951-7715/11/4/007
  • [9] Sliding bifurcations: A novel mechanism for the sudden onset of chaos in dry friction oscillators
    Di Bernardo, M
    Kowalczyk, P
    Nordmark, A
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (10): : 2935 - 2948
  • [10] Switchings, bifurcations, and chaos in DC/DC converters
    di Bernardo, M
    Garofalo, F
    Glielmo, L
    Vasca, F
    [J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 1998, 45 (02) : 133 - 141
12