A Melnikov analysis on a family of second order discontinuous differential equations

Fuente: arXiv
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Main Authors: Novaes, Douglas D., Silva, Luan V. M. F.
Format: Preprint
Published: 2023
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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