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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.
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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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