Propagation dynamics of a nonlocal time-space periodic reaction-diffusion model with delay
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In this article , a non-local time-space periodic reaction diffusion model with age structure is considered, and the authors show that transition semi-waves of the model in the non-monotone case exist when their wave speed is above a critical speed.Abstract:
<p style='text-indent:20px;'>This paper is concerned with a nonlocal time-space periodic reaction diffusion model with age structure. We first prove the existence and global attractivity of time-space periodic solution for the model. Next, by a family of principal eigenvalues associated with linear operators, we characterize the asymptotic speed of spread of the model in the monotone and non-monotone cases. Furthermore, we introduce a notion of transition semi-waves for the model, and then by constructing appropriate upper and lower solutions, and using the results of the asymptotic speed of spread, we show that transition semi-waves of the model in the non-monotone case exist when their wave speed is above a critical speed, and transition semi-waves do not exist anymore when their wave speed is less than the critical speed. It turns out that the asymptotic speed of spread coincides with the critical wave speed of transition semi-waves in the non-monotone case. In addition, we show that the obtained transition semi-waves are actually transition waves in the monotone case. Finally, numerical simulations for various cases are carried out to support our theoretical results.</p> read more
Citations
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Journal ArticleDOI
Spatial Dynamics of a Nonlocal Reaction-Diffusion Epidemic Model in Time-Space Periodic Habitat
Ming-Zhen Xin,Bin-Guo Wang +1 more
TL;DR: In this article , a partially degenerate reaction-diffusion epidemic model with latent period in time-space periodic habitat was studied and a threshold result on the global stability of either zero or the positive time space periodic solution in terms of the basic reproduction ratio was obtained.
Journal ArticleDOI
Propagation dynamics of a nonlocal reaction-diffusion system
Bang-Sheng Han,De-Yu Kong +1 more
TL;DR: In this paper , the propagation dynamics of a three-species reaction-diffusion system with nonlocal diffusion was investigated and the diffusion kernel functions symmetry and asymmetry were obtained by comparison principle.
References
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Xing Liang,Xiao-Qiang Zhao +1 more
TL;DR: In this article, the theory of asymptotic speeds of spread and monotone traveling waves is established for a class of discrete and continuous-time semlows and is applied to a functional differential equation with diffusion, a time-delayed lattice population model and a reaction-diffusion equation in an infinite cylinder.
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On spreading speeds and traveling waves for growth and migration models in a periodic habitat.
TL;DR: It is shown that the methods previously used to obtain asymptotic spreading results and sometimes the existence of traveling waves for a discrete-time recursion with a translation invariant order preserving operator can be extended to a recursions with a periodic order preservingoperator.