On the dynamical behavior of some algal allelopathic competitions in chemostat-like environment

Abstract

The dynamics of some algal allelopathic competitions taking place in a laboratory chemostat-like environment are analyzed. Our main results concern the global asymptotic stability of some biologically meaningful steady-state solutions and have been obtained by means of limiting systems theory and construction of suitable Liapunov functions. In particular one of these results completely explains the outcome of several experiments recently performed and illustrated in Fergola et al. (Ecol Model 208:205-214, 2007) on the competition between C. vulgaris and P. subcapitata. Numerical simulations confirm the analytical results and show that saddle-node bifurcation phenomena can appear.

A competition model in the chemostat with allelopathy and substrate inhibition

“…37]), which in mathematical terms means changing the functional response rather than adding an additional substance to the model, and -allelopathic inhibition which is the production of a chemical by one species that negatively impacts another species. For a discussion on the various models on inhibition and Allelopathy the reader is referred to the survey [21] and the references therein, see also [3,5,6,8,9,24] for recent works.…”

“…Fergola et al [8,9] produced a model of the chemostat with Allelopathy and substrate inhibition, where the growth rate of the first competitor is Andrews.…”

Robust Set Stabilization and Its Instances for Open Quantum Systems

“…The publication of the work of Lure and a book [26] by Lassall and Lefschetz brought Lyapunov's work to the attention of the larger control engineering community in the early 1960s. Several stability concepts such as finite-time stability, [27] Lipschitz stability, [28] partial stablity, [29] and practical stability [26] have been investigated based on Lyapunov's great work in the 20th century. In 2002, Phooi et al [30] further proposed the broad-sense Lyapunov function and generalized the notation of stability in the sense of Lyapunov.…”

A competition model with dynamically allocated toxin production in the unstirred chemostat

“…The study on the problem of the influence of toxicants both on the growth of one population and on the competition of two species for a critical nutrient has received considerable attention in the past decades (see, e.g., [1,2,5,11,13,21,22,18,19,20,1374 HUA NIE, SZE-BI HSU AND JIANHUA WU 28,30,31]). Particularly, there has been a lot of interest in the so called allelopathic competitions between species (see, e.g., [2,5,16,21,22,18,24,28]).…”

“…This suggests a possible mechanism for coexistence. Rigorous mathematical analysis of allelopathic competition models with quorum sensing in the well-stirred chemostat-like environment can be found, for example, in [1,11,13].…”