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Abstract:
Chen [2016a, 2016b] studied global dynamics of the Filippov systems <(x)double over dot> + (alpha + beta x(2))(x)over dot + x +/- sgn(x) = 0, respectively. To study the global dynamics of <(x)double over dot>+(alpha+beta x(2))(x)over dot +/- x +/- sgn(x) = 0 completely, since the dynamics of <(x)double over dot>+(alpha+beta x(2))(x)over dot-x-sgn(x) = 0 is very simple, we are only interested in the global dynamics of <(x)double over dot>+(alpha+beta x(2))(x)over dot - x + sgn(x) = 0 in this paper. Firstly, we use Briot-Bouquet transformations and normal sector methods to discuss these degenerate equilibria at infinity. Secondly, we discuss the number of limit cycles completely. Then, the sufficient and necessary conditions of existence of the heteroclinic loop are found. To estimate the upper bound of the heteroclinic loop bifurcation function on parameter space, a result on the amplitude of a unique limit cycle of a discontinuous Lienard system is given. Finally, the complete bifurcation diagram and all global phase portraits are presented. The global dynamic property of system <(x)double over dot>+(alpha+beta x(2))(x) over dot-x+sgn(x) = 0 is totally different from systems <(x)double over dot>+(alpha+beta x(2))(x)+x +/- sgn(x) = 0.
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INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN: 0218-1274
Year: 2020
Issue: 7
Volume: 30
2 . 8 3 6
JCR@2020
1 . 9 0 0
JCR@2023
ESI Discipline: MATHEMATICS;
ESI HC Threshold:50
JCR Journal Grade:2
CAS Journal Grade:3
Cited Count:
WoS CC Cited Count: 2
SCOPUS Cited Count: 1
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 0
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