Traveling waves in a diffusive predator–prey system of Holling type: Point-to-point and point-to-periodic heteroclinic orbits |
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| Institution: | 1. Department of Mathematics, Foshan University, Foshan 528000, PR China;2. School of Mathematics, South China Normal University, Guangzhou 510631, PR China;1. School of Mathematics and Physics, University of South China, Hengyang, 421001, China;2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John''s, Newfoundland, A1C 5S7, Canada;1. School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, PR China;2. School of Mathematical Sciences, Soochow University, Suzhou 215006, PR China;3. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, PR China;1. Department of Mathematics and Statistics, University of Missouri-Kansas City, Kansas City, MO 64110-2499, USA;2. Department of Mathematics, Clarkson University, Potsdam, NY, 13699-5815, USA |
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| Abstract: | We demonstrate the existence of small amplitude traveling wave train solutions and two kinds of traveling wave solutions of a diffusive predator–prey system with general Holling type functional response, i.e., the analysis shows the existence of periodic orbits, point-to-point connection and point-to-periodic orbit connection. Also, the minimal wave speed for biological invasion is obtained. The method or techniques used here can be extended to a diffusive predator–prey system with more general functional response, not only the Holling type. |
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