A computation method for non-autonomous systems with discontinuous characteristics

被引：7

作者：

Miino, Yuu ^{[1
]}

Ito, Daisuke ^{[2
]}

Ueta, Tetsushi ^{[3
]}

机构：

[1] Univ Tokushima, Adv Technol & Sci, Syst Innovat Engn, Tokushima 7708506, Japan

[2] Univ Shiga Prefecture, Sch Engn, Dept Elect Syst Engn, Hikone, Shiga 5228533, Japan

[3] Univ Tokushima, Ctr Adm Informat Technol, Tokushima 7708506, Japan

来源：

CHAOS SOLITONS & FRACTALS | 2015年 / 77卷

关键词：

Bifurcation phenomena; Numerical analysis; Nonlinear non-autonomous system; Discontinuity; BIFURCATION; MODEL;

D O I：

10.1016/j.chaos.2015.06.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We propose a computation method to obtain bifurcation sets of periodic solutions in non-autonomous systems with discontinuous properties. If the system has discontinuity for the states and/or the vector field, conventional methods cannot be applied. We have developed a method for autonomous systems with discontinuity by taking the Poincare mapping on the switching point in the preceded study, however, this idea does not work well for some non-autonomous systems with discontinuity. We overcome this difficulty by extending the system to an autonomous system. As a result, bifurcation sets of periodic solutions are solved accurately with a shooting method. We show two numerical examples and demonstrate the corresponding laboratory experiment. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：277 / 285

页数：9

共 15 条

[1] Bifurcations in two-dimensional piecewise smooth maps - Theory and applications in switching circuits
Banerjee, S
Ranjan, P
Grebogi, C
[J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2000, 47 (05) : 633 - 643
[2] 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
[3] Grazing and border-collision in piecewise-smooth systems: A unified analytical framework
di Bernardo, M
Budd, CJ
Champneys, AR
[J]. PHYSICAL REVIEW LETTERS, 2001, 86 (12) : 2553 - 2556
[4] A piecewise linear suspension bridge model: Nonlinear dynamics and orbit continuation
Doole, SH
Hogan, SJ
[J]. DYNAMICS AND STABILITY OF SYSTEMS, 1996, 11 (01): : 19 - 47
[5] Ito D, 2010, P NOLTA2010 POL, P627
[6] Controlling Chaos of Hybrid Systems by Variable Threshold Values
Ito, Daisuke
Ueta, Tetsushi
Kousaka, Takuji
Imura, Jun'ichi
Aihara, Kazuyuki
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2014, 24 (10):
[7] Simple model of spiking neurons
Izhikevich, EM
[J]. IEEE TRANSACTIONS ON NEURAL NETWORKS, 2003, 14 (06): : 1569 - 1572
[8] BIFURCATION OF PERIODIC RESPONSES IN FORCED DYNAMIC NONLINEAR CIRCUITS - COMPUTATION OF BIFURCATION VALUES OF THE SYSTEM PARAMETERS
KAWAKAMI, H
[J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1984, 31 (03): : 248 - 260
[9] Kawakami H., 1979, Proceedings of the 1979 International Symposium on circuits and systems, P44
[10] Kawakami H, 1992, P RIMS C STRUCT BIF, P39

← 1 2 →