The Beverton-Holt Dynamic Equation
The Cushing-Henson conjectures on time scales are presented and verified. The central part of these conjectures asserts that based on a model using the dynamic Beverton-Holt equation, a periodic environment is deleterious for the population. The proof technique is as follows. First, the Beverton-Holt equation is identified as a logistic dynamic equation. The usual substitution transforms this equation into a linear equation. Then the proof is completed using a recently established dynamic version of the generalized Jensen inequality.
H. Warth and M. Bohner, "The Beverton-Holt Dynamic Equation," Applicable Analysis, Taylor & Francis Ltd., Aug 2007.
The definitive version is available at http://dx.doi.org/10.1080/00036810701474140
Mathematics and Statistics
Keywords and Phrases
Complex Variables; Computational Numerical Analysis; Differential Equations; Fourier Analysis; Functional Analysis; Integral Transforms & Equations; Mathematical Analysis; Mathematical Numerical Analysis; Operator Theory; Real Functions; Sequences & Series; Special Functions
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