Lotka-Volterra Model With Alternating Predator-prey Reversals in the Left-right Political Spectrum

Predator-prey reversal: "In marine benthic communities, rock lobsters, Jasus lalandii, usually represent a keystone predator in diverse ecosystems. However, if its common prey, the whelk (Burnupena sp.), greatly outnumbers the rock lobster, it may result in an alternative stable ecosystem where rock lobsters are killed by whelks, which dominate in the alternated ecosystem."

What if this system were bistable and looped indefinitely?

The basic schematics of this system remind me of the alternation between left and right political dominance over time due to changes in a political landscape which shifts between two stable political paradigms, with the intermediate stance being centrism.

The point at which the left-right political paradigm reversal is initiated might be explained by some kind of population threshold which, when reached, causes the 'predator' entity to become complacent and decline, or the 'prey' entity to adapt to the new paradigm and compete until reversal is achieved.

If this kind of model can represent the left right political system, then there are three possible outcome cases:

1. After some period of alternation between states, one of the populations consumes the other entirely resulting in a single population in the system (A dominant-party political system which will devolve into a de jure, or defacto, single-party system). [Left XOR Right]
2. Both populations survive, alternating between the two states indefinitely (A two-party political system much like USA, and somewhat Australia today. The two major parties require eachother for survival, yet still compete against eachother. This occurs when the left attacks the right and the right attacks the left in a bistable system). [Left OR Right]<br>
3. Both populations decline while alternating over time until they both approach zero (A two-party political system in which both parties decline in popularity until both parties are eventually phased out. In a political system, this phase-out would be achieved with either mutualism between the left and right allowing centrism to establish dominance, or both are phased out to make room for some external party through colonisation, mass migration or conquest). [Left XNOR Right]

Any ideas on what might trigger the reversal of left and right political roles? My guess is that counter-culture plays a HUGE role in this. People get really sick of repetition of trends, and eventually need a change in paradigm (to regulate between diversity and homogeneity, if anything). You can almost feel the predator-prey role reversal threshold being reached in certain political arms races, such as the 2016 election, or more recently the recent rise to power of climate alarmism.

I wonder if a Lotka-Volterra model with alternating predator prey relationship is even a thing.