A Kolmogorov-type competition model with multiple coexistence states and its applications to plant competition for sunlight
It is demonstrated that a Kolmogorov-type competition model featuring species allocation and gain functions can possess multiple coexistence states. Two examples are constructed: one in which the two competing species possess rectangular allocation functions but distinct gain functions, and the other in which one species has a rectangular allocation function, the second species has a bi-rectangular allocation function, and the two species share a common gain function. In both examples, it is shown that the species nullclines may intersect multiple times within the interior of the first quadrant, thus creating both locally stable and unstable equilibrium points. These results have important applications in the study of plant competition for sunlight, in which the allocation functions describe the vertical placement of leaves for two competing species, and the gain functions represent rates of photosynthesis performed by leaves at different heights when shaded by overlying leaves belonging to either species. (C) 2008 Elsevier Inc. All rights reserved.
Journal of Mathematical Analysis and Applications
"A Kolmogorov-type competition model with multiple coexistence states and its applications to plant competition for sunlight" (2008). Faculty Bibliography 2000s. 502.