Competitive coexistence and competitive exclusion for a nonlinear community with delay effect and impulsive birth

• The phenomena of competitive coexistence and competitive exclusion of a nonlinear competitive community under environmental fluctuation and species response delay is investigated systematically.
• (1) A nonlinear competition community based on the Lotka–Volterra interaction system is constructed. The time-dependent community parameters and impulsive fertility activity of community species are introduced so as to reflect the seasonality of physical environments, the biological phenomena, such as nonlinear competition patterns as well as response delay of the species, are also involved.
• (2) The theoretical formula that are essentially equivalent to the phase plane analysis results on competitive coexistence and exclusions of the community are established, which confirms the validity of applying the phase plane analysis technique to general non-autonomous nonlinear community in life, physics and social science.
• (3) It is demonstrated that slight deviation of the response delay from zero and small perturbation of the coupling strength of competition from linear interaction pattern have little impact on competitive coexistence of the community, but acute changes have distinct negative influence on the competitive coexistence of the community.

By constructing a population model of multi-species competition, a community with nonlinear interaction relationship is investigated, in which the species’ response delay and environmental fluctuation effects (i.e., seasonal fluctuation of resource supplies and species’ reproductive activities) on population are considered. Firstly, the conditions about competitive coexistence (i.e., persistence of all species) and competitive exclusion (i.e., only partial of species, but not all, keep persistence) of the community are established, and the underlying ecological mechanism of these results are analyzed. Secondly, by some illustrative examples, the interactive effects of nonlinear competition, species’ response delay and environmental fluctuation on the structure of community are explored. It is demonstrated that small response delay and slight deviation of nonlinear competition indexes from 1 have little impact on the coexistence of community, but acute changes have distinct negative influence on community coexistence. This reveals to us that parameter perturbations of natural communities should keep in an appropriate range, which is of great significance in conservation and restoration biology.