Dynamical Systems Under Constant Organization II: Homogeneous Growth Functions of Degree $p = 2$

Qualitative analysis is presented for a system of differential equations, which play an important role in a theory of molecular self-organization: \[\dot x_i = \left( {\sum\limits_{p = 1}^n {k_{ip} x_p - \sum\limits_p {\sum\limits_q {k_{pq} x_p x_q } } } } \right)x_i ,\quad i = 1, \cdots ,n\]. Besides the general case two simplifications are treated: (1) the norihyperbolic case: $k_{ij} \mathop > \limits_ = 0(k_{ii} = 0)$ and (2) cyclic symmetry: $k_{ij} = k_{i + 1,j + 1} $. Criteria for cooperation and exclusion are derived.