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Travelling waves of a predator¨Cprey model with a spatiotemporal delay Qintao Gan Mathematical Methods in the Applied Sciences Volume 37, Issue 3, pages 408¨C419, February 2014 |
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ganqintao: ½ð±Ò+15, ¡ï¡ï¡ï¡ï¡ï×î¼Ñ´ð°¸ 2014-05-07 19:18:59
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ganqintao: ½ð±Ò+15, ¡ï¡ï¡ï¡ï¡ï×î¼Ñ´ð°¸ 2014-05-07 19:18:59
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¼ìË÷ÁË, ¼ûÏÂÃæÏêϸÐÅÏ¢ MATHEMATICAL METHODS IN THE APPLIED SCIENCES ¾í: 37 ÆÚ: 3 Ò³: 408-419 DOI: 10.1002/mma.2800 ³ö°æÄê: FEB 2014 ²é¿´ÆÚ¿¯ÐÅÏ¢ ÕªÒª This paper is concerned with the existence of traveling waves to a predator-prey model with a spatiotemporal delay. By analyzing the corresponding characteristic equations, the local stability of a positive steady state and each of boundary steady states are established, and the existence of Hopf bifurcation at the positive steady state is also discussed. By constructing a pair of upper-lower solutions and by using the cross-iteration method as well as the Schauder's fixed-point theorem, the existence of a traveling wave solution connecting the semi-trivial steady state and the positive steady state is proved. Numerical simulations are carried out to illustrate the main theoretical results. Copyright (c) 2013 John Wiley & Sons, Ltd. ¹Ø¼ü´Ê ×÷Õ߹ؼü´Ê:predator-prey model; traveling waves; upper-lower solutions; spatiotemporal delay; partial monotonicity KeyWords Plus:REACTION-DIFFUSION SYSTEMS; STAGE STRUCTURE; TIME DELAYS; STABILITY; FRONTS; EQUATION; BIFURCATION; COMPETITION; TERMS ×÷ÕßÐÅÏ¢ ͨѶ×÷ÕßµØÖ·: Gan, QT (ͨѶ×÷Õß) Shijiazhuang Mech Engn Coll, Dept Basic Sci, 97 Heping West Rd, Shijiazhuang 050003, Hebei Province, Peoples R China. µØÖ·: [ 1 ] Shijiazhuang Mech Engn Coll, Dept Basic Sci, Shijiazhuang 050003, Hebei Province, Peoples R China µç×ÓÓʼþµØÖ·:ganqintao@sina.com »ù½ð×ÊÖúÖÂл »ù½ð×ÊÖú»ú¹¹ ÊÚȨºÅ National Natural Science Foundation of China 10671209 11071254 ²é¿´»ù½ð×ÊÖúÐÅÏ¢ ³ö°æÉÌ WILEY-BLACKWELL, 111 RIVER ST, HOBOKEN 07030-5774, NJ USA Àà±ð / ·ÖÀà Ñо¿·½Ïò:Mathematics Web of Science Àà±ð:Mathematics, Applied ÎÄÏ×ÐÅÏ¢ ÎÄÏ×ÀàÐÍ:Article ÓïÖÖ:English Èë²ØºÅ: WOS:000329559200010 ISSN: 0170-4214 µç×Ó ISSN: 1099-1476 ÆÚ¿¯ÐÅÏ¢ Impact Factor (Ó°ÏìÒò×Ó): Journal Citation Reports® ÆäËûÐÅÏ¢ IDS ºÅ: 287RF Web of Science ºËÐĺϼ¯ÖÐµÄ "ÒýÓõIJο¼ÎÄÏ×": 33 Web of Science ºËÐĺϼ¯ÖÐµÄ "±»ÒýƵ´Î": 0 |

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