Bifurcation analysis of a competitive system with general toxic production and delayed toxic effects. Issue 18 (December 2022)

• Record Type: Journal Article
• Authors: Mu, Yu; Lo, Wing-Cheong
• Is Part Of: Journal of the Franklin Institute. Volume 359:Issue 18(2022)
• Page Start: 10884
• Page End: 10906
• Publication Date: 2022-12
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2022.05.019
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: Population interaction may release poisonous chemicals to inhibit other species' growth in the ecosystem, especially for the competitive populations. The negative effect of toxic chemical substances may not display immediately and appear with time lag during the species' growth. In this work, we investigate a competitive system with the delayed toxic effects of the chemicals from species interaction. Theoretical results obtained in this work help us reveal the delayed toxic factors on species' growth. We first consider the existence and the stability of the equilibria. The influence of delay terms on the positive steady state is validated. The delayed toxic effects here will contribute to the oscillation for the concentration of species when the value of time delay passes through a critical point. Besides, the stability of periodic solutions from the Hopf bifurcation and the direction of the Hopf bifurcation are also determined. Finally, several numerical examples are provided to validate the theoretical conclusions.