A Melnikov analysis on a family of second order discontinuous differential equations
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913476129062912 |
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| author | Novaes, Douglas D. Silva, Luan V. M. F. |
| author_facet | Novaes, Douglas D. Silva, Luan V. M. F. |
| contents | This paper aims to provide a Melnikov-like function that governs the existence of periodic solutions bifurcating from period annuli in certain families of second-order discontinuous differential equations of the form $\ddot{x}+α\; \textrm{sign}(x)=ηx+\varepsilon \;f(t,x,\dot{x})$. This family has attracted considerable attention from researchers, particularly in the analysis of specific instances of $f(t,x,\dot{x})$. The study of this type of differential equation is motivated by its significance in modeling systems with abrupt state changes, both in natural and engineering contexts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02738 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Melnikov analysis on a family of second order discontinuous differential equations Novaes, Douglas D. Silva, Luan V. M. F. Dynamical Systems 34A36, 34C15, 34C25, 37G15 This paper aims to provide a Melnikov-like function that governs the existence of periodic solutions bifurcating from period annuli in certain families of second-order discontinuous differential equations of the form $\ddot{x}+α\; \textrm{sign}(x)=ηx+\varepsilon \;f(t,x,\dot{x})$. This family has attracted considerable attention from researchers, particularly in the analysis of specific instances of $f(t,x,\dot{x})$. The study of this type of differential equation is motivated by its significance in modeling systems with abrupt state changes, both in natural and engineering contexts. |
| title | A Melnikov analysis on a family of second order discontinuous differential equations |
| topic | Dynamical Systems 34A36, 34C15, 34C25, 37G15 |
| url | https://arxiv.org/abs/2312.02738 |