Abstract
This article studies the minimal wave speed of traveling wave solutions in an integrodifference predator-prey system that does not have the comparison principle. By constructing generalized upper and lower solutions and utilizing the theory of asymptotic spreading, we show the minimal wave speed of traveling wave solutions modeling the invasion process of two species by presenting the existence and nonexistence of nonconstant traveling wave solutions with any wave speeds.
Highlights
Discrete time systems are widely used to model the evolution of species without overlapping generations, and some novel dynamics including chaos have been presented comparing with the corresponding continuous time models; see some models by Beddington et al [1], Hofbauer et al [2], and Weide et al [3] and monographs by Murray [4]
We show the asymptotic behavior of traveling wave solutions and nonexistence of traveling wave solutions, which indicate a minimal wave speed of nontrivial traveling wave solutions
Minimal wave speed of traveling wave solutions of evolutionary systems is very important in modeling the spatial expansion of individuals under consideration [26, 27]
Summary
Discrete time systems are widely used to model the evolution of species without overlapping generations, and some novel dynamics including chaos have been presented comparing with the corresponding continuous time models; see some models by Beddington et al [1], Hofbauer et al [2], and Weide et al [3] and monographs by Murray [4]. After rescaling, one predator-prey system takes the form as follows: Discrete Dynamics in Nature and Society. Since Weinberger [16], the propagation dynamics of integrodifference equations has been widely studied, of which the abstract results can be applied to continuous time models [17]. When ki is of Gaussian type, Li and Li [22] established the existence of traveling wave solutions connecting (0, 0) with the coexistence state if the wave speed is larger than the threshold, which is finished by constructing upper and lower solutions. Only the large wave speed is investigated, what is the threshold on the existence of nontrivial traveling wave solutions? We remove condition (8) to study the threshold that determines the existence or nonexistence of nontrivial traveling wave solutions for all positive wave speeds.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
