Modulo periodic Poisson stable solutions of quasilinear differential equations

TL;DR

This paper introduces a new recurrence concept in function spaces and proves the existence and stability of modulo periodic Poisson stable solutions in quasilinear differential equations, supported by numerical simulations.

Contribution

It presents a novel recurrence property and demonstrates the existence and stability of Poisson stable solutions in quasilinear systems, with applications to oscillations.

Findings

Existence of modulo periodic Poisson stable solutions.

Asymptotic stability of these solutions.

Numerical simulations illustrating the solutions.

Abstract

We introduce a new type of recurrence in the space of continuous and bounded functions. The property is easily verifiable, and can be considered for differential equations. This time, the existence and asymptotic stability of modulo periodic Poisson stable solutions for quasilinear systems are proved. The significant novelty of the research is the numerical simulation of the functions, which is stemmed from dynamical traditions of trigonometric functions, and contributes to applications of Poisson stable oscillations.