Is My System of ODEs <i>k</i>-Cooperative?

A linear dynamical system is called positive if its flow maps the non-negative orthant to itself. More precisely, it set of vectors with zero sign variations k-positive up k -1 nonlinear k-cooperative variational system, which a time-varying k-positive. These systems have special asymptotic properties. For example, was recently shown that strong 2-cooperative satisfy Poincaré-Bendixson property. Positivity and k-positivity are easy verify in terms sign-pattern matrix dynamics. However, these conditions not invariant under coordinate transformation. natural question determine given n-dimensional We study this problem for two kinds transformations: permutations scaling by signature matrix. any n ≥ 4 ε {2, ...,n - 21}, we provide graph-theoretic necessary sufficient condition such transformations. describe an application our results specific class Lotka-Volterra systems.