Dynamical phase diagrams of a love capacity constrained prey-predator model

TL;DR

This paper models complex love relationships using a prey-predator Verhulst-Lotka-Volterra system, revealing the instability of loving multiple people simultaneously and conditions for stable friendly relationships.

Contribution

It introduces a novel prey-predator model for love dynamics with three persons, analyzing various love scenarios and their stability.

Findings

Loving more than one person simultaneously is unstable.

Certain conditions lead to friendly, non-romantic relationships.

Flow diagrams illustrate the dynamic behaviors.

Abstract

One interesting question in love relationships is: finally, what and when is the end of this love relationship? Using a prey-predator Verhulst-Lotka-Volterra (VLV) model we imply cooperation and competition tendency between people in order to describe a "love dilemma game". We select the most simple but immediately most complex case for studying the set of nonlinear differential equations, i.e. that implying three persons, being at the same time prey and predator. We describe four different scenarios in such a love game containing either a one-way love or a love triangle. Our results show that it is hard to love more than one person simultaneously. Moreover, to love several people simultaneously is an unstable state. We find some condition in which persons tend to have a friendly relationship and love someone in spite of their antagonistic interaction. We demonstrate the dynamics by displaying flow diagrams.