Speaker: Prof. Bingtuan Li,
University of Louisville

Title: Existence of traveling waves for integral recursions with nonmonotone growth functions.

Abstract: Abstract: In this talk we will discuss integral recursion models for the growth and spread of a synchronized single-species population. It is well known that if there is no overcompensation in the fecundity function, the recursion has an asymptotic spreading speed, and that this speed can be characterized as the speed of the slowest non-constant traveling wave solution. It is also known that a class of integral recursions with overcompensation still have asymptotic spreading speeds. This presentation will give a large subclass of these models with overcompensation for which the spreading speed can still be characterized as the slowest speed of a non-constant traveling wave. We will show numerical simulations indicating that , depending on the properties of the fecundity function,the tails of the waves may approach the carrying capacity monotonically, may approach the carrying capacity in an oscillatory manner, or may oscillate continually about the carrying capacity, with its values bounded above and below by computable positive numbers. (Joint work with Hans Weinberger and Mark Lewis)