Asymptotic stability of tri-trophic food chains sharing a common resource.
One of the key results of the food web theory states that the interior equilibrium of a tri-trophic food chain described by the Lotka-Volterra type dynamics is globally asymptotically stable whenever it exists. This article extends this result to food webs consisting of several food chains sharing a common resource. A Lyapunov function for such food webs is constructed and asymptotic stability of the interior equilibrium is proved. Numerical simulations show that as the number of food chains increases, the real part of the leading eigenvalue, while still negative, approaches zero. Thus the resilience of such food webs decreases with the number of food chains in the web.
Mathematical Institute, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic. Electronic address: vrkoc@math.cas.cz.
Ivo
I
Vrkoč
Institute of Entomology, Biology Center, Czech Academy of Sciences, Branišovská 31, 370 05 České Budějovice, Czech Republic; Department of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia, Branišovská 1760, 370 05 České Budějovice, Czech Republic. Electronic address: vlastimil.krivan@gmail.com.
Vlastimil
V
Křivan
D000818:Animals; D044822:Biodiversity; D017753:Ecosystem; D020387:Food Chain; D055641:Mathematical Concepts; D008954:Models, Biological
Competition; Food webs; Lyapunov function; Resilience; Stability