Distributed Delays Stabilize Ecological Feedback Systems

Christian Eurich, Andreas Thiel, and Lorenz Fahse
(Please use for correspondence this email).

Submission date: 05. Apr. 2005
Pages: 6
published in: Physical review letters, 94 (2005) 15, art-no. 158104 
DOI number (of the published article): 10.1103/PhysRevLett.94.158104
PACS-Numbers: 02.30.Ks, 87.10.+e, 87.23.Cc
Keywords and phrases: biological feedback systems
Download preprint: PDF (814 kB), PS ziped (725 kB)

Abstract:
We consider the effect of distributed delays in predator-prey models and ecological food webs. Whereas the occurrence of delays in population dynamics is usually regarded a destabilizing factor leading to the extinction of species, we here demonstrate complementarily that delay distributions yield larger stability regimes than single delays. Food webs with distributed delays closely resemble non-delayed systems in terms of ecological stability measures. Thus, we state that dependence of dynamics on multiple instances in the past is an important, but so far underestimated factor for stability in dynamical systems.