ISSN:
1432-1416
Keywords:
Key words: Bifurcation diagram
;
Chaos
;
Chemostat
;
Food chain
;
Existence and stability
;
Limit cycle
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Abstract. The dynamic behaviour of food chains under chemostat conditions is studied. The microbial food chain consists of substrate (non-growing resources), bacteria (prey), ciliates (predator) and carnivore (top predator). The governing equations are formulated at the population level. Yet these equations are derived from a dynamic energy budget model formulated at the individual level. The resulting model is an autonomous system of four first-order ordinary differential equations. These food chains resemble those occuring in ecosystems. Then the prey is generally assumed to grow logistically. Therefore the model of these systems is formed by three first-order ordinary differential equations. As with these ecosystems, there is chaotic behaviour of the autonomous microbial food chain under chemostat conditions with biologically relevant parameter values. It appears that the trajectories on the attractors consists of two superimposed oscillatory behaviours, a slow one for predator–top predator and a fast one for the prey–predator on one branch at which the top predator increases slowly. In some regions of the parameter space there are multiple attractors.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002850050088
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