Equations ( )-(61d) represent the outer or steady-state solutions after s 2 reaches s * 2 and c 2 reaches c * 2 . Collectively, in the four-dimensional phase space, the system approaches a manifold M ε,δ * . Denoting the c 1 -, s 2 -and c 2 -nullclines as N c1 , N s2 and N c2 respectively, the leading order approximation to M ε,δ * is expressible in terms of the intersecting nullclines: