Journal
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
Volume 21, Issue 2, Pages -Publisher
SPRINGER BASEL AG
DOI: 10.1007/s12346-021-00554-x
Keywords
Piecewise smooth system; T-periodic perturbation; Generalized heteroclinic loop; Sliding periodic orbit; Bifurcation
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Funding
- National Natural Science Foundation of China [12171056]
- Natural Science Foundation of Hunan Province, China [2021JJ30698]
- Research Foundation of Education Bureau of Hunan Province, China [20B018]
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This work focuses on the bifurcation of periodic orbits in a perturbed piecewise smooth system with a generalized heteroclinic loop connecting a hyperbolic critical point and a quadratic tangential singularity. By constructing displacement functions dependent on the perturbation parameter epsilon and time t, the conditions for the existence of a homoclinic loop and a sliding generalized heteroclinic loop are obtained. A concrete example is provided to demonstrate the occurrence of corresponding phenomena under suitable perturbations of the generalized heteroclinic loop.
This work deals with the periodic orbit bifurcations of a T-periodic perturbed piecewise smooth system whose unperturbed part has a generalized heteroclinic loop connecting a hyperbolic critical point and a quadratic tangential singularity. By constructing several displacement functions that depend on perturbation parameter epsilon and time t, sufficient conditions of the existence of a homoclinic loop and a sliding generalized heteroclinic loop (that is a generalized heteroclinic loop a part of which lies on the switching manifold) are obtained. As the application, we give a concrete example to show that under suitable perturbations of the generalized heteroclinic loop the corresponding phenomena can appear.
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