@article{78594dc97d874927b65b9a5e20154d8c,
title = "Topological horseshoes of traveling waves for a fast-slow predator-prey system",
abstract = "We show the existence of a set of periodic traveling waves in a system of two scalar reaction diffusion equations, which is in one-to-one correspondence with a full shift on two symbols. We use a novel combination of rigorous numerical computations and the topological techniques of the Conley index theory. This approach is quite general, and this paper is intended as a demonstration of its usefulness and applicability.",
keywords = "Conley index theory, Predator-prey system, Rigorous computation, Singular perturbation, Symbolic dynamics, Traveling wave",
author = "Marcio Gameiro and Tom{\'a}{\v s} Gedeon and William Kalies and Hiroshi Kokubu and Konstantin Mischaikow and Hiroe Oka",
note = "Funding Information: This work was partially supported by NSF grant INT-0089631 and by JSPS Japan-U.S. Cooperative Science Program. M. G. was partially supported by NSF grants DMS-0107396, and INT-0089631, DARPA, and CAPES, Brazil. T. G. was partially supported by NSF-BITS grant 0129895, NIH-NCRR grant PR16445 and NSF/NIH grant W0467. W. K. was partially supported by NSF grants DMS-997331, DMS-0511208, and DOE grant 97888. H. K. was partially supported by JSPS Grant-in-Aid for Scientific Research (No. 14340055, No. 17340045). K. M. was partially supported by NSF grants DMS-0511115, DMS-0107396, DMS-0443827, and INT-0089631, and DOE grant 97891, and DARPA. H. O. was partially supported by JSPS Grant-in-Aid for Scientific Research (No. 14540219, No. 17540206). We would like to thank Pawe{\l} Pilarczyk for his assistance with the CAPD Library. On the occasion of Pavol Brunovsky`{\textquoteright}s 70th Birthday.",
year = "2007",
month = sep,
doi = "10.1007/s10884-006-9013-6",
language = "English (US)",
volume = "19",
pages = "623--654",
journal = "Journal of Dynamics and Differential Equations",
issn = "1040-7294",
publisher = "Springer New York",
number = "3",
}