# Finding cones for K-cooperative systems

## TL;DR

This paper introduces a numerical cone finding algorithm to analyze nonlinear systems via differential positivity, offering a new tool for studying multi-stability beyond traditional Lyapunov methods.

## Contribution

The paper presents a novel cone finding algorithm that enhances the analysis of nonlinear systems through differential positivity, demonstrated on complex multi-stable and controlled oscillator examples.

## Key findings

- Effective in identifying cones for nonlinear systems
- Applicable to multi-stable and oscillatory dynamics
- Provides a numerical alternative to Lyapunov analysis

## Abstract

We design and test a cone finding algorithm to robustly address nonlinear system analysis through differential positivity. The approach provides a numerical tool to study multi-stable systems, beyond Lyapunov analysis. The theory is illustrated on two examples: a consensus problem with some repulsive interactions and second order agent dynamics, and a controlled duffing oscillator.