The Beverton–Holt dynamic equation

Abstract

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.

Keywords:

• Cushing–Henson conjecture;
• Time scales;
• Dynamic equation;
• Logistic equation;
• Beverton–Holt equation;
• Jensen inequality

Keywords:

• Mathematics Subject Classifications (2000):
• 39A10;
• 39A11;
• 39A12;
• 39A20;
• 34C25