2006/06/30 by Frank M. Hilker, Frank M. Hilker, Frank H. Westerhoff +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Environmental Science · Medicine · Physics and Astronomy · #Chaos control and synchronization #Chaotic #Ecosystem dynamics and resilience #Extinction (optical mineralogy) #Extinction probability #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear system #Outbreak #Population #Simple (philosophy) #nlin.CD #q-bio.PE
paper · pdf · doi:10.1086/518949
published as American Naturalist 170, 232-241 (2007) · 10 pages, 6 figures
openalex publication_date 2007/07/24 · arxiv created 2007/08/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Interactions in ecological communities are inherently nonlinear and can lead to complex population dynamics including irregular fluctuations induced by chaos. Chaotic population dynamics can exhibit violent oscillations with extremely small or large population abundances that might cause extinction and recurrent outbreaks, respectively. We present a simple method that can guide management efforts to prevent crashes, peaks, or any other undesirable state. At the same time, the irregularity of the dynamics can be preserved when chaos is desirable for the population. The control scheme is easy to implement because it relies on time series information only. The method is illustrated by two examples: control of crashes in the Ricker map and control of outbreaks in a stage-structured model of the flour beetle Tribolium. It turns out to be effective even with few available data and in the presence of noise, as is typical for ecological settings.