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author:

Pu, Jiao (Pu, Jiao.) [1] | Chen, Xiaofeng (Chen, Xiaofeng.) [2] (Scholars:陈晓锋) | Chen, Hebai (Chen, Hebai.) [3] | Xia, Yong-Hui (Xia, Yong-Hui.) [4]

Indexed by:

EI SCIE

Abstract:

In [Chen et al., 2020], the third author and other coauthors studied global dynamics of the following system: {(x)overdot = y - [b(1)x - b(2)/2 (vertical bar x + 1 vertical bar - vertical bar x - 1 vertical bar)], (y)overdot = - [b(3)x + b(2)/2 (vertical bar x + 1 vertical bar - vertical bar x - 1 vertical bar) - b(4]), in the parameter region {( b(1), b(2), b(3), b(4)) is an element of R-4 : b(2) < 0, b(4) not equal 0}. To study completely the piecewise linear system, we consider the parameter region {( b(1), b(2), b(3), b(4)) is an element of R-4 : b(2) > 0, b(4) not equal 0} in this paper. Firstly, we study the local dynamics, such as the bifurcations of equilibria (including the equilibrium at infinity). Secondly, the number and stability of limit cycles are studied completely. Then, we analyze the existence of upper and lower saddle connections and homoclinic loops. Moreover, we show that there are no heteroclinic loops in this parameter region. Finally, we give the bifurcation diagram and all global phase portraits on the Poincare disc are given as well as some numerical examples.

Keyword:

bifurcation diagram global phase portrait limit cycle Piecewise linear differential system saddle connection

Community:

  • [ 1 ] [Pu, Jiao]Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350116, Fujian, Peoples R China
  • [ 2 ] [Chen, Xiaofeng]Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350116, Fujian, Peoples R China
  • [ 3 ] [Chen, Hebai]Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
  • [ 4 ] [Xia, Yong-Hui]Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

Reprint 's Address:

  • 陈晓锋

    [Chen, Xiaofeng]Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350116, Fujian, Peoples R China

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Source :

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

ISSN: 0218-1274

Year: 2021

Issue: 2

Volume: 31

2 . 4 5

JCR@2021

1 . 9 0 0

JCR@2023

ESI Discipline: MATHEMATICS;

ESI HC Threshold:36

JCR Journal Grade:2

CAS Journal Grade:3

Cited Count:

WoS CC Cited Count: 4

SCOPUS Cited Count: 4

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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