Asymptotic spreading of time periodic competition diffusion systems

Bo, Wei-Jian; Guo, Lin

doi:10.3934/dcdsb.2018116

Cited by 2 publications

(8 citation statements)

References 36 publications

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“…then our conclusion holds by Lemma 2.2 if (u, v), (u, v) are a pair of upper and lower solutions of system(5). Now, we verify the inequalities in Definition 2.1, and the inequalities on u(x, t), v(x, t) are clear.…”

supporting

confidence: 61%

“…where t > 0 is large enough such that u(x) ≤ u(x, 0), ϕ 1 (t) is defined by (10). Similar to the proof of Lemma 3.2, we can easily verify that (u, v), (u, v) are a pair of upper and lower solutions of system (5).…”

Section: Xinjian Wang and Guo Linmentioning

confidence: 73%

“…Main results. In this section, we shall study system (5) in two cases. The first case is that v is stronger than u in the sense of d 2 r 2 > d 1 r 1 , and the second one is that u is stronger than v in the sense of d 1 r 1 − b 1 V > d 2 r 2 + a 2 U .…”

Section: Lemma 22 Is Clear By the Classical Theory Of Reaction-diffumentioning

confidence: 99%

“…To prove the convergence of (u(x, t), v(x, t)), we first prove the following result by the idea in [4,5].…”

Section: Xinjian Wang and Guo Linmentioning

confidence: 99%

“…In this paper, we obtain the bounds of spreading speed of the predator and the prey in two cases by constructing suitable upper and lower solutions and auxiliary equations, applying the generalized eigenvalue and further combining the theory of asymptotic spreading of scalar equations with comparison principle. To study the long time behavior of solutions, we prove that the solution of (2) converges to the positive T -periodic solution by the idea in [4,5]. These results show that either the predator or the prey has a spreading speed that is determined by the linearized…”

mentioning

confidence: 91%

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Asymptotic spreading for a time-periodic predator-prey system

Wang¹,

Lin²

2019

Communications on Pure &Amp; Applied Analysis

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This paper is concerned with asymptotic spreading for a timeperiodic predator-prey system where both species synchronously invade a new habitat. Under two different conditions, we show the bounds of spreading speeds of the predator and the prey, which is proved by the theory of asymptotic spreading of scalar equations, comparison principle and generalized eigenvalue. We show either the predator or the prey has a spreading speed that is determined by the linearized equation at the trivial steady state while the spreading speed of the other also depends on the interspecific nonlinearity. From the viewpoint of population dynamics, our results imply that the predator may play a negative effect on the spreading of the prey while the prey may play a positive role on the spreading of the predator. t→∞ sup |x|>(c * + )t u(x, t) = 0 for any given > 0,u(x, t) > 0 for any given ∈ (0, c * ).Clearly, the definition of spreading speed states that if an observer were to move to the right or left at a fixed speed greater (less) than c * , then the local population density u(x, t) would eventually look like 0 (greater than 0) [41], and it also describes the speed at which the geographic range of the new population expands in population dynamics. In the case of monotone semiflows and cooperative systems, 2000 Mathematics Subject Classification. Primary: 35K45, 35K57; Secondary: 92D25.

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supporting

confidence: 61%

Section: Xinjian Wang and Guo Linmentioning

confidence: 73%

Section: Lemma 22 Is Clear By the Classical Theory Of Reaction-diffumentioning

confidence: 99%

“…To prove the convergence of (u(x, t), v(x, t)), we first prove the following result by the idea in [4,5].…”

Section: Xinjian Wang and Guo Linmentioning

confidence: 99%

mentioning

confidence: 91%

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Asymptotic spreading for a time-periodic predator-prey system

Wang¹,

Lin²

2019

Communications on Pure &Amp; Applied Analysis

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Traveling waves and spreading properties for a reaction-diffusion competition model with seasonal succession*

2021

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In this paper, we investigate the propagation dynamics of a reaction–diffusion competition model with seasonal succession in the whole space. Under the weak competition condition, the corresponding kinetic system admits a globally stable positive periodic solution ( u ^ ( t ) , v ^ ( t ) ) . By the method of upper and lower solutions and the Schauder fixed point theorem, we first obtain the existence and nonexistence of traveling wave solutions connecting (0, 0) to ( u ^ ( t ) , v ^ ( t ) ) . Then we use the comparison arguments to establish the spreading properties for a large class of solutions.

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Asymptotic spreading of time periodic competition diffusion systems

Cited by 2 publications

References 36 publications

Asymptotic spreading for a time-periodic predator-prey system

Asymptotic spreading for a time-periodic predator-prey system

Traveling waves and spreading properties for a reaction-diffusion competition model with seasonal succession*

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