Traveling Waves Connecting Equilibrium and Periodic Orbit for a Delayed Population Model on a Two-Dimensional Spatial Lattice
2016 ◽
Vol 26
(03)
◽
pp. 1650049
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Keyword(s):
This paper is concerned with the existence of fast traveling waves connecting an equilibrium and a periodic orbit in a delayed population model with stage structure on a two-dimensional spatial lattice, under the assumption that the corresponding ODEs have heteroclinic orbits connecting an equilibrium point and a periodic solution. In this work, we rewrite the mixed functional differential equation as an integral equation in a Banach space and analyze the corresponding linear operator. Our approach eventually reduces a singular perturbation problem to a regular perturbation problem. The existence of traveling wave solution therefore is obtained by using the Liapunov–Schmidt method and implicit function theorem.
2012 ◽
Vol 13
(4)
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pp. 1873-1890
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Keyword(s):
2010 ◽
Vol 13
(3)
◽
pp. 559-575
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Keyword(s):
2007 ◽
Vol 73
(4)
◽
pp. 592-618
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Keyword(s):
2013 ◽
Vol 03
(01)
◽
pp. 27-36
2000 ◽
1980 ◽
Vol 58
◽
pp. 661-666