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

J. Hofbauer, P. Schuster, K. Sigmund and R. Wolff
SIAM Journal on Applied Mathematics
Vol. 38, No. 2 (Apr., 1980), pp. 282-304
Stable URL: http://www.jstor.org/stable/2101020
Page Count: 23
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Dynamical Systems Under Constant Organization II: Homogeneous Growth Functions of Degree p = 2
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Abstract

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 = \bigg(\sum^n_{p = 1} k_{ip}x_p - \sum_p\sum_q k_{pq}x_px_q \bigg)x_i,\quad i = 1, \cdots, n.$ Besides the general case two simplifications are treated: (1) the nonhyperbolic case: kij ≥ 0 (kii = 0) and (2) cyclic symmetry: kij = ki + 1, j + 1. Criteria for cooperation and exclusion are derived.

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