Abstract
Competition is one of the most common form in ecological systems, which plays important roles in population dynamics. However, the influences of competition on persistence of populations remain unclear when space effect is included. In this paper, we investigated a predator-prey model with competition and spatial diffusion. Based on pattern formations and time series of populations, we found that competitions induce the persistence of populations, which denies competitive exclusion principle. Moreover, we testify the robustness of these effects. Our results also suggest that space may lead to the emergence of new phenomenon in ecosystems.
Highlights
Ecological system is an important part of the real world, and populations constitute the ecological system[1,2,3]
We can restrict our analysis of pattern formation to one distribution
We investigated a predator-prey model with competition and spatial diffusion
Summary
Ecological system is an important part of the real world, and populations constitute the ecological system[1,2,3]. From biological point of view, this principle suggests that two competitive species can not survive at the same time or in the same niche. In other words, it implies that competition behaviors play negative roles in the persistence of the populations. In previous work[27,28,29], it was found that competition may induce the populations to exhibit rich pattern structures, including mixed state of spotted and stripe pattern, labyrinth pattern and spotted pattern. We want to check whether competition behaviors have adverse impact in the persistence of the populations when space is included. We want to show the functions of pattern transition on the stability of the populations systems.
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