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Summary: Chaos in Delay Differential Equations with
Applications in Population Dynamics
Alfonso Ruiz-Herrera
Departamento de Matem´atica Aplicada
Facultad de Ciencias 18071
Universidad de Granada, Spain
e-mail: alfonsoruiz@ugr.es
October 3, 2011
Abstract
We develop a geometrical method to detect the presence of chaotic dynamics in
delay differential equations. An application to the classical Lotka-Volterra model
with delay is given.
2000 MSC. 34C25, 54H20,92D25.
Key words: Topological horseshoes, Delay, Stretching Along Paths, Global Continuation of horse-
shoes, Predator-prey systems .
1 Introduction
For the last decades, delay differential equations have been considered as a natural
framework to model many real world phenomena. These equations usually arise
in models of population dynamics, neural networks or electrical engineer since the
usage of time delay naturally appears to express the maturation period of a concrete
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