Abstract
A Melnikov like condition for the persistence of a periodic and grazing solution under autonomous perturbation is derived for discontinuous systems. For this purpose, the grazing Poincaré map is derived. Then its fixed point is studied to determine desired solutions leading to Melnikov like conditions. Theory is illustrated by a concrete example modelling such type of solutions.
Flaviano Battelli: This chapter has been performed within the activity of GNAMPA-INdAM-CNR.
Michal Fečkan: Partially supported by the Slovak Research and Development Agency under the contract No. APVV-18-0308 and by the Slovak Grant Agency VEGA No. 1/0358/20 and No. 2/0127/20.
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We thank the referees for careful reading and valuable comments that helped to improve the chapter.
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Battelli, F., Fečkan, M. (2020). On the Poincaré-Andronov-Melnikov Method for Modelling of Grazing Periodic Solutions in Discontinuous Systems. In: Dutta, H. (eds) Mathematical Modelling in Health, Social and Applied Sciences. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-2286-4_7
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DOI: https://doi.org/10.1007/978-981-15-2286-4_7
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