Bifurcation Analysis in a Class of Piecewise Nonlinear Systems with a Nonsmooth Heteroclinic Loop
2018 ◽
Vol 28
(02)
◽
pp. 1850026
Keyword(s):
We consider the bifurcation in a class of piecewise polynomial systems with piecewise polynomial perturbations. The corresponding unperturbed system is supposed to possess an elementary or nilpotent critical point. First, we present 17 cases of possible phase portraits and conditions with at least one nonsmooth periodic orbit for the unperturbed system. Then we focus on the two specific cases with two heteroclinic orbits and investigate the number of limit cycles near the loop by means of the first-order Melnikov function, respectively. Finally, we take a quartic piecewise system with quintic piecewise polynomial perturbation as an example and obtain that there can exist ten limit cycles near the heteroclinic loop.
2021 ◽
Vol 31
(09)
◽
pp. 2150123
Keyword(s):
2012 ◽
Vol 22
(12)
◽
pp. 1250296
◽
2016 ◽
Vol 26
(11)
◽
pp. 1650180
◽
2010 ◽
Vol 20
(05)
◽
pp. 1379-1390
◽
2016 ◽
Vol 26
(01)
◽
pp. 1650009
◽
Keyword(s):
2019 ◽
Vol 29
(05)
◽
pp. 1950072
Keyword(s):
2011 ◽
Vol 21
(11)
◽
pp. 3341-3357