INFLUENCE OF A SPATIAL STRUCTURE ON THE LONG TIME BEHAVIOR OF A COMPETITIVE LOTKA-VOLTERRA TYPE SYSTEM

作者：Leman Helene^*; Meleard Sylvie; Mirrahimi Sepideh

来源：Discrete and Continuous Dynamical Systems-Series B, 2015, 20(2): 469-493.

DOI：10.3934/dcdsb.2015.20.469

• Structured populations
• phenotypical and spatial structure
• parabolic Lotka-Volterra type systems
• stationary solutions
• long time behavior

To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on type structured populations, to models of populations structured by type and space, considering diffusion and nonlocal competition between individuals?
We study a nonlocal competitive Lotka-Volterra type system, describing a spatially structured population which can be either monomorphic or dimorphic. Considering spatial diffusion, intrinsic death and birth rates, together with death rates due to intraspecific and interspecific competition between the individuals, leading to some integral terms, we analyze the long time behavior of the solutions. We first prove existence of steady states and next determine the long time limits, depending on the competition rates and the principal eigen-values of some operators, corresponding somehow to the strength of traits. Numerical computations illustrate that the introduction of a new mutant population can lead to the long time evolution of the spatial niche.

• 出版日期2015-3