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Construction of analytically solvable models for interacting speciesThe basic form of a model representation for systems of n interacting biological species is a set of essentially nonlinear autonomous ordinary differential equations. A generic canonical expression for the rate functions in the equations is reported which permits the analytical general solution to be obtained by elementary computation. It is shown that a general analytical solution is directly obtainable for models where the rate functions are prescribed by the generic canonical expression from the outset. Some illustrative examples are given which demonstrate that the generic canonical expression can be used to construct analytically solvable models for two interacting species with limit-cycle dynamics as well as for a three-species interdependence.
Document ID
19770054942
Document Type
Reprint (Version printed in journal)
Authors
Rosen, G. (Drexel University Philadelphia, Pa., United States)
Date Acquired
August 9, 2013
Publication Date
January 1, 1976
Publication Information
Publication: Bulletin of Mathematical Biology
Volume: 38
Subject Category
NUMERICAL ANALYSIS
Funding Number(s)
CONTRACT_GRANT: NSG-3090
Distribution Limits
Public
Copyright
Other