Propagation dynamics for a spatially periodic integrodifference competition model

Wu, Ruiwen; Zhao, Xiao-Qiang

doi:10.1016/j.jde.2018.01.039

Cited by 9 publications

(5 citation statements)

References 40 publications

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“…We now focus on the integrodifference systems. When the spatial inhomogeneous is involved, there are some conclusions on monotone/cooperative integrodifference systems in periodic habitat, see Ding et al [4], Fang et al [8], Weinberger [40], Wu and Zhao [43] and references cited therein. When the time periodic is concerned, Liang et al [15] studied the asymptotic spreading and traveling wave solutions of an abstract monotone integrodifference equation, and the results can be applied to other models generating monotone semiflows.…”

Section: Guo Lin and Shuxia Panmentioning

confidence: 99%

Periodic traveling wave solutions of periodic integrodifference systems

Lin¹,

Pan²

2020

Discrete &Amp; Continuous Dynamical Systems - B

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This paper is concerned with the periodic traveling wave solutions of integrodifference systems with periodic parameters. Without the assumptions on monotonicity, the existence of periodic traveling wave solutions is deduced to the existence of generalized upper and lower solutions by fixed point theorem and an operator with multi steps. The asymptotic behavior of periodic traveling wave solutions is investigated by the stability of periodic solutions in the corresponding initial value problem or the corresponding difference systems. To illustrate our conclusions, we study the periodic traveling wave solutions of two models including a scalar equation and a competitive type system, which do not generate monotone semiflows. The existence or nonexistence of periodic traveling wave solutions with all positive wave speeds is presented, which implies the minimal wave speeds of these models.

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Section: Guo Lin and Shuxia Panmentioning

confidence: 99%

Periodic traveling wave solutions of periodic integrodifference systems

Lin¹,

Pan²

2020

Discrete &Amp; Continuous Dynamical Systems - B

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“…Zhang and Zhao [29] also established the existence and global stability of bistable waves for discrete-time two species competition recursion systems with bistable structure. Recently, Wu and Zhao [28] studied the existence of spatially periodic traveling wave, single spreading speed and the linear determinacy for a class of intergrodifference competition models in a periodic habitat. For the competitive-cooperative reaction-diffusion system with nonlocal delays,…”

Section: Introductionmentioning

confidence: 99%

Existence and stability of traveling waves for a competitive-cooperative recursion system

Bao,

2020

ejde

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This article concerns the existence and global stability of bistable traveling waves for a competitive-cooperative recursion system. We first show that the spatially homogeneous system associated with the competitive-cooperative recursion system admits a bistable structure. Then using the theory of bistable waves for monotone semiflows and a dynamical system approach, we prove that there exists an unique and global stable traveling wave solution connecting two stable equilibria for such recursion system under appropriate conditions. For more information see https://ejde.math.txstate.edu/Volumes/2020/88/abstr.html

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“…See [14] and [26,Sec.3,4] for some early contributions. An important application are propagation dynamics like spreading speeds and traveling waves (see [16,17,32] and the literature mentioned there). Other questions concern stability and instability of the zero function, the extinction equilibrium (critical domain size), of interior equilibria and periodic solutions (see [15,Sec.5.4], [18,22,23] and the literature cited there).…”

mentioning

confidence: 99%

Discrete-time dynamics of structured populations via Feller kernels

Thieme¹

2022

DCDS-B

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Feller kernels are a concise means to formalize individual structural transitions in a structured discrete-time population model. An iteroparous populations (in which generations overlap) is considered where different kernels model the structural transitions for neonates and for older individuals. Other Feller kernels are used to model competition between individuals. The spectral radius of a suitable Feller kernel is established as basic turnover number that acts as threshold between population extinction and population persistence. If the basic turnover number exceeds one, the population shows various degrees of persistence that depend on the irreducibility and other properties of the transition kernels.

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Propagation dynamics for a spatially periodic integrodifference competition model

Cited by 9 publications

References 40 publications

Periodic traveling wave solutions of periodic integrodifference systems

Periodic traveling wave solutions of periodic integrodifference systems

Existence and stability of traveling waves for a competitive-cooperative recursion system

Discrete-time dynamics of structured populations via Feller kernels

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