Related Experiment Video
Updated: Aug 15, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Food chain chaos due to transcritical point
1Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA. bdeng@math.unl.edu
Abstract:
Chaotic dynamics of a classical prey-predator-superpredator ecological model are considered. Although much is known about the behavior of the model numerically, very few results have been proven analytically. A new analytical result is obtained. It is demonstrated that there exists a subset on which a singular Poincare map generated by the model is conjugate to the shift map on two symbols. The existence of such a Poincare map is due to two conditions: the assumption that each species has its own time scale ranging from fast for the prey to slow for the superpredator, and the existence of transcritical points, leading to the classical mathematical phenomenon of Pontryagin's delay of loss of stability. This chaos generating mechanism is new, neither suspected in abstract form nor recognized in numerical experiments in the literature.
Related Concept Videos
Radical Chain-Growth Polymerization: Chain Branching
Path Between Thermodynamics States
Circular Shaft - Stresses in Linear Range
Stress Concentrations in Circular Shafts
Transmission Shafts: Problem Solving
Next, use bending moment diagrams for the shaft to...
The Chain Rule: Problem Solving

