The open dense conjecture on eventually slow oscillations of the differential equation with delayed negative feedback

TL;DR

This paper addresses a longstanding open dense conjecture concerning the behavior of differential equations with delayed negative feedback, specifically focusing on their eventual slow oscillations, using advanced semiflow methods.

Contribution

It introduces a novel application of strongly order-preserving semiflow techniques with high-rank cones to resolve the open dense conjecture.

Findings

Successfully proves the open dense conjecture for delayed negative feedback equations.

Demonstrates the effectiveness of semiflow methods in analyzing oscillatory behavior.

Provides new insights into the dynamics of delayed differential equations.

Abstract

In this paper, we show how to use the approach of the strongly order-preserving semiflow with respect to high-rank cones to solve the open dense conjecture on eventually slow oscillations of the differential equation with delayed negative feedback.