Asymptotic periodicity of the Volterra equation with infinite delay

作者：Wang Jinliang^*; Zhou Li; Tang Yanbin

来源：Nonlinear Analysis-Theory Methods & Applications, 2008, 68(2): 315-328.

DOI：10.1016/j.na.2006.10.050

• Volterra
• asymptotic periodicity
• delay
• existence
• uniqueness

For some species, hereditary factors have great effects on their population evolution, which can be described by the well-known Volterra model. A model developed is investigated in this article, considering the seasonal variation of the environment, where the diffusive effect of the population is also considered. The main approaches employed here are the upper-lower solution method and the monotone iteration technique. The results show that whether the species dies out or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the hereditary effects. The evolution of the population may show asymptotic periodicity, provided a certain condition is satisfied for the above factors.

• 出版日期2008-1-15
• 单位中国科学院海洋研究所