JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (10): 97-105.doi: 10.6040/j.issn.1671-9352.0.2022.633

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Existence of traveling wave solutions for a diffusive predator-prey model

Hang ZHANG(),Yujuan JIAO*(),Jinmiao YANG   

  1. College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China
  • Received:2022-11-14 Online:2023-10-20 Published:2023-10-17
  • Contact: Yujuan JIAO E-mail:y211530520@stu.xbmu.edu.cn;jsjyj@xbmu.edu.cn

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Abstract:

In this paper, we discuss the existence of traveling wave solutions for a diffusive predator-prey model. Firstly, using linearization method, we prove non-existence of traveling wave solutions for the model with c < c*. Secondly, we establish the existence of weak traveling wave solutions with c≥c* by applying upper and lower solution method and Schauder's fixed point theorem. Moreover, utilizing Lyapunov function and LaSalle's invariance principle, we obtain that the weak traveling wave solutions for the model are traveling wave solutions under the suitable conditions. Finally, the numerical experiments support the validity of our theoretical results.

Key words: traveling wave solution, predator-prey model, upper and lower solution, Schauder's fixed point theorem, Lyapunov function

CLC Number: 

  • O175.26

Table 1

Parameter value of System (1.2)"

参数 r1 r2 η1 η2 c1 c2 d K1 K2 m
取值 0.01 0.10 0.15 0.5 0.5 0.5 0.4 2 2 0.5

Table 2

Parameter value of System (1.3)"

参数 r1 r2 η1 η2 c1 c2 d K1 K2 m c
取值 0.01 0.10 0.15 0.5 0.5 0.5 0.4 2 2 0.5 2

Fig.1

Population density changes of three species in System (1.3)"

Fig.2

Population density changes of three species in System (1.2)"

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