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arXiv · 2312.02738

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

Douglas D. Novaes·Luan V. M. F. Silva
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Abstract

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 $\ddot{x}+\alpha\; \textrm{sign}(x)=\eta x+\varepsilon \;f(t,x,\dot{x})$. 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.

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Douglas D. Novaes, Luan V. M. F. Silva. 2023-12-05. A Melnikov analysis on a family of second order discontinuous differential equations. https://doi.org/10.1007/s40863-024-00436-5

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