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| TRAVELING WAVE SOLUTIONS FOR A PREDATOR-PREY MODEL WITH BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE |
| Zhuanling Gao,Xiangkui Zhao,Zhihong Zhao |
| (School of Mathematics and Physics, University of Science Technology Beijing, Beijing 100083, PR China) |
| DOI： |
| Abstract: |
| In this paper, we study a class of predator-prey models with Beddington-DeAngelis functional response. And the predator equation has singularity in zero prey population, where a smoothing auxiliary function is introduced to overcome it. Our aim is to see if the predator and prey can eventually survive
when an alien predator enters the habitat of an existing prey by employing traveling wave solutions, based on the upper and lower solutions and Schauder's fixed point theorem. In addition, the non-existence of traveling wave solutions is discussed by the comparison principle. At the same time, some simulations are carried out to further verify the results. |
| Key words: predator-prey model; Beddington-DeAngelis; traveling wave solution; existence |