Minimal Wave Speed in a Delayed Lattice Dynamical System with Competitive Nonlinearity
This paper deals with the minimal wave speed of delayed lattice dynamical systems without monotonicity in the sense of standard partial ordering in R2. By constructing upper and lower solutions appealing to the exponential ordering, we prove the existence of traveling wave solutions if the wave spee...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/1950767 |
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| _version_ | 1832566771230441472 |
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| author | Fuzhen Wu |
| author_facet | Fuzhen Wu |
| author_sort | Fuzhen Wu |
| collection | DOAJ |
| description | This paper deals with the minimal wave speed of delayed lattice dynamical systems without monotonicity in the sense of standard partial ordering in R2. By constructing upper and lower solutions appealing to the exponential ordering, we prove the existence of traveling wave solutions if the wave speed is not smaller than some threshold. The nonexistence of traveling wave solutions is obtained when the wave speed is smaller than the threshold. Therefore, we confirm the threshold is the minimal wave speed, which completes the known results. |
| format | Article |
| id | doaj-art-97539cc43da440bbb97710a411d6f79f |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-97539cc43da440bbb97710a411d6f79f2025-02-03T01:03:22ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/19507671950767Minimal Wave Speed in a Delayed Lattice Dynamical System with Competitive NonlinearityFuzhen Wu0Department of Basic, Zhejiang University of Water Resources and Electric Power Hangzhou, Zhejiang 310018, ChinaThis paper deals with the minimal wave speed of delayed lattice dynamical systems without monotonicity in the sense of standard partial ordering in R2. By constructing upper and lower solutions appealing to the exponential ordering, we prove the existence of traveling wave solutions if the wave speed is not smaller than some threshold. The nonexistence of traveling wave solutions is obtained when the wave speed is smaller than the threshold. Therefore, we confirm the threshold is the minimal wave speed, which completes the known results.http://dx.doi.org/10.1155/2019/1950767 |
| spellingShingle | Fuzhen Wu Minimal Wave Speed in a Delayed Lattice Dynamical System with Competitive Nonlinearity Discrete Dynamics in Nature and Society |
| title | Minimal Wave Speed in a Delayed Lattice Dynamical System with Competitive Nonlinearity |
| title_full | Minimal Wave Speed in a Delayed Lattice Dynamical System with Competitive Nonlinearity |
| title_fullStr | Minimal Wave Speed in a Delayed Lattice Dynamical System with Competitive Nonlinearity |
| title_full_unstemmed | Minimal Wave Speed in a Delayed Lattice Dynamical System with Competitive Nonlinearity |
| title_short | Minimal Wave Speed in a Delayed Lattice Dynamical System with Competitive Nonlinearity |
| title_sort | minimal wave speed in a delayed lattice dynamical system with competitive nonlinearity |
| url | http://dx.doi.org/10.1155/2019/1950767 |
| work_keys_str_mv | AT fuzhenwu minimalwavespeedinadelayedlatticedynamicalsystemwithcompetitivenonlinearity |