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Chen [2016a, 2016b] studied global dynamics of the Filippov systems ? + (α + βx2)? + x ±sgn(x)=0, respectively. To study the global dynamics of ? + (α + βx2)? ± x ±sgn(x)=0 completely, since the dynamics of ? + (α + βx2)? - x -sgn(x) = 0 is very simple, we are only interested in the global dynamics of ? + (α + βx2)? - 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 Liénard system is given. Finally, the complete bifurcation diagram and all global phase portraits are presented. The global dynamic property of system ? + (α + βx2)? - x + sgn(x) = 0 is totally different from systems ? + (α + βx2)? + x ±sgn(x) = 0. © 2020 World Scientific Publishing Company.
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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 HC Threshold:50
JCR Journal Grade:2
CAS Journal Grade:3
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