What Is an Attracting Heteroclinic Cycle in a 3D Population Model?

[Tryingtolearn]

Hopefully this is a quick questions. I'm trying to describe what an attracting heteroclinic cycle is but not sure really how to describe it or what it means. I have a 3-dimensional population model x(t), y(t), z(t), which has a phase portrait that spirals from one equilibrium point to three other equilibrium points on a plane. I understand that at t go to infinity that the slution curve spends more and more time around each one of the three equilibrium points as it passes by.

So back to my problem, I'm not sure how to describe this in context of an attracting heteroclinic cycle because I have no idea and can't find a good definition of that a heteroclinic cycle is.

Thanks for your help.

 

[M98Ranger]

An attracting heteroclinic cycle is a type of dynamic behavior in a system where the solution curve follows a path that connects multiple equilibrium points in a non-repetitive manner. In your 3-dimensional population model, it appears that the solution curve spirals from one equilibrium point to three other equilibrium points on a plane. This spiral behavior is characteristic of a heteroclinic cycle. Additionally, the fact that the solution curve spends more and more time around each equilibrium point as it passes by is indicative of the attracting nature of the cycle. This means that the solution curve is drawn towards each equilibrium point, making it an attracting heteroclinic cycle. In summary, an attracting heteroclinic cycle is a type of dynamic behavior where the solution curve connects multiple equilibrium points in a non-repetitive manner and is drawn towards each point, leading to a spiral-like path.