Here, we use an adaptive snowdrift game as an example to illustrate how coupled dynamics influence each other and explicit coupled transitions in the form of disconnected to connected network transition(structural) highly cooperative to lower cooperative population(functional) segregated phase to mixed-character phase(population characteristics frozen to continously evolving(dynamical) how one could approach such problems analytically what to look at in formulating a theory and its validity what a proper theory can inform us about the properties of the systemHere, we • use an adaptive snowdrift game as an example to illustrate… -- how coupled dynamics influence each other and explicit coupled transitions in the form of • disconnected to connected network transition (structural) • highly cooperative to lower cooperative population (functional) • segregated phase to mixed-character phase (population characteristics) • frozen to continously evolving (dynamical) -- how one could approach such problems analytically -- what to look at in formulating a theory and its validity -- what a proper theory can inform us about the properties of the system