Dynamic behaviors of a discrete Lotka-Volterra competitive system with the effect of toxic substances and feedback controls

Abstract

By noting the fact that the intrinsic growth rate are not positive everywhere, we revisit Lotka-Volterra competitive system with the effect of toxic substances and feedback controls. The corresponding results about permanence and extinction for the species given in (Chen and Chen in Int. J. Biomath. 8(1):1550012, 2015) are extended. Furthermore, a very important fact is found in our results, that is, the feedback controls and toxic substances have no effect on the permanence and extinction of species. Moreover, we also derive sufficient conditions for the global stability of positive solutions. Finally, some numerical simulations show the feasibility of our main results.

Species and Other Evolving Lineages as Feedback Systems

“…23 In addition to the termite example already given, there is well-known focus on feedback relations in some other areas of biology, where metapopulation evolving lineages are not the object of study. Consider chemotaxis networks in bacterial navigation (e.g., Wadhams and Armitage 2004) and both ecological (e.g., Miao et al 2017) and eco-evolutionary dynamics in communities (e.g., Becks et al 2012). Closer to the present topic, there is a long though relatively spotty history, beginning with Darwin (Robertson and Grant 1996a, 10) and leading up through Fisher (1930) and others to some contemporary researchers (e.g., Caporale and Doyle 2013; Lehtonen and Kokko 2012; Robertson andGrant 1996a, 1996b), of claiming that feedback relations are important to understanding natural selection within a population.…”

Dynamical analysis of almost periodic solution for a multispecies predator-prey model with mutual interference and time delays

“…The dynamical property of a multispecies predator-prey system is much more complex than the system with only two or three species, and the analytical methods are very different [11,[20][21][22].…”