Abstract
By observing that the n-tuple of rate functionsQ(c) is orthogonal to the c-space gradients of each of the (n - 1) constants of the motion Φ v (c), a generic canonical expression for the rate functions is given in terms of the exterior product of the gradients of the (n - 1) Φ v 's. For models withQ so prescribed from the outset, an analytical general solution is obtainable directly for the system of autonomous ordinary differential equations dc/dt =Q(c). Thus, the generic canonical expression for the rate functions can be utilized to construct analytically solvable models for interacting biological species, as ilIus~rated by examples here.
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Rosen, G. Construction of analytically solvable models for interacting species. Bltn Mathcal Biology 38, 193–197 (1976). https://doi.org/10.1007/BF02471755
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DOI: https://doi.org/10.1007/BF02471755