  Many complex engineering systems network together functional elements and
balance demand loads (e.g.information on data networks, electric power on
grids). This allows load spikes to be shifted and avoid a local overload. In
mobile wireless networks, base stations(BSs) receive data demand and shift high
loads to neighbouring BSs to avoid the outage. The stability of cascade load
balancing is important because unstable networks can cause high inefficiency.
The research challenge is to prove the stability conditions for any arbitrarily
large, complex, and dynamic network topology, and for any balancing dynamic
function. Our previous work has proven the conditions for stability for
stationary networks near equilibrium for any load balancing dynamic and
topology. Most current analyses in dynamic complex networks linearize the
system around the fixed equilibrium solutions. This approach is insufficient
for dynamic networks with changing equilibrium and estimating the Region of
Attraction(ROA) is needed. The novelty of this paper is that we compress this
high-dimensional system and use Level Set Methods (LSM) to estimate the ROA.
Our results show how we can control the ROA via network topology (local degree
control) as a way to configure the mobility of transceivers to ensure the
preservation of stable load balancing.
