Hah alien invasions would be interesting...
Does the model you are exploring have variables/logic for the death and birth of states you can implement? I imagine the stability of the model may be less, but I can imagine a few ways to implement birth/death that may not cause instability (I haven't looked at the papers you link to). Mainly by using proportionality as your weights, e.g. The larger the state, the more prone to fracture, the smaller the state, the more prone to death.