Global stability of a delay differential equations model of plankton allelopathy

摘要

In this paper, we consider a delay differential equations model of plankton allelopathy. Using an iterative method, the global stability of the interior equilibrium point of the system is investigated, which shows that toxic substances are harmless for the stability of the interior equilibrium point. The results we obtained improve and complement those of Chattopadhyay [J. Chattopadhyay, Effect of toxic substances on a two-species competitive system, Ecol. Model. 84 (1996) 287–289], Samanta [G.P. Samanta, A two-species competitive system under the influence of toxic substances, Appl. Math. Comput. 216 (2010) 291–299] and Mukhopadhyay et al. [A. Mukhopadhyay, J. Chattopadhyay, P.K. Tapaswi, A delay differential equations model of plankton allelopathy, Math. Biosci. 149 (1998) 167–189]. We also present some examples to verify our main result.