  We consider a model of adversarial dynamics consisting of three populations,
labelled Blue, Green and Red, which evolve under a system of first order
nonlinear differential equations. Red and Blue populations are adversaries and
interact via a set of Lanchester combat laws. Green is divided into three
sub-populations: Red supporters, Blue supporters and Neutral. Green support for
Red and Blue leads to more combat effectiveness for either side. From Green's
perspective, if either Red or Blue exceed a size according to the capacity of
the local population to facilitate or tolerate, then support for that side
diminishes; the corresponding Green population reverts to the neutral
sub-population, who do not contribute to combat effectiveness of either side.
The mechanism for supporters deciding if either Blue or Red are too big is
given by a logistic-type interaction term. The intent of the model is to
examine the role of influence in complex adversarial situations typical in
counter-insurgency, where victory requires a genuine balance between
maintaining combat effectiveness and support from a third party whose backing
is not always assured.
