Abstract
This paper is mainly concerned with the new types of entire solutions which are different from pulsating fronts of Lotka-Volterra competition systems with asymmetric dispersal in spatially periodic habitats. The asymmetry of kernel function leads to a great influence on the profile of pulsating fronts and the sign of wave speeds, which gives rise to the properties of the entire solution more complex and diverse. We first give a relationship between the critical speeds c ⁎ ( ξ ) and c ⁎ ( − ξ ) , corresponding to the minimal speeds of two pulsating fronts propagating in the direction of ξ and − ξ , respectively. Then, the exponential behavior of pulsating fronts as they approach their limiting states is obtained. Finally, by considering the interactions of two different pulsating fronts coming from two opposite/same directions and applying the super-/subsolutions techniques as well as the comparison principle, we establish the existence and various qualitative properties of some different types of entire solutions defined for all time and whole space. Moreover, we give some numerical simulations to describe intuitively these obtained entire solutions.
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