@article{c041efe2c77d421595455d454852d895,
title = "Pinned Solutions in a Heterogeneous Three-Component FitzHugh–Nagumo Model",
abstract = "We analyse pinned front and pulse solutions in a singularly perturbed three-component FitzHugh–Nagumo model with a small jump-type heterogeneity. We derive explicit conditions for the existence and stability of these type of pinned solutions by combining geometric singular perturbation techniques and an action functional approach. Most notably, in certain parameter regimes we can explicitly compute the pinning distance of a localised solution to the defect.",
keywords = "Calculus of variations, Defects, Existence, Localised defect solutions, Reaction–diffusion equations, Singular perturbations, Stability",
author = "{van Heijster}, Peter and Chen, {Chao Nien} and Yasumasa Nishiura and Takashi Teramoto",
note = "Funding Information: Acknowledgements PvH thanks the National Changhua University of Education in Taiwan, the National Center for Theoretical Sciences in Taiwan, and Tohoku University in Japan for their hospitality. CNC is grateful for the warm hospitality of Queensland University of Technology in Australia. YN and TT also thank Queensland University of Technology in Australia and the National Tsing-Hua University in Taiwan for their hospitality. The authors also acknowledge support from the Mathematics Research Promotion Center in Taiwan and they note that part of this research was finalised during the first joint Australia-Japan workshop on dynamical systems with applications in life sciences at Queensland University of Technology in Australia. Funding Information: PvH thanks the National Changhua University of Education in Taiwan, the National Center for Theoretical Sciences in Taiwan, and Tohoku University in Japan for their hospitality. CNC is grateful for the warm hospitality of Queensland University of Technology in Australia. YN and TT also thank Queensland University of Technology in Australia and the National Tsing-Hua University in Taiwan for their hospitality. The authors also acknowledge support from the Mathematics Research Promotion Center in Taiwan and they note that part of this research was finalised during the first joint Australia-Japan workshop on dynamical systems with applications in life sciences at Queensland University of Technology in Australia. Funding Information: PvH was supported under the Australian Research Councils Discovery Early Career Researcher Award funding scheme DE140100741. Part of the work was done when CNC was visiting QUT and he is grateful for the support by the Ministry of Science and Technology of Taiwan. YN is partially supported by KAKENHI 26247015 and JSPS A3 Foresight Program. TT is partially supported by KAKENHI Grant-in-Aid for Scientific Research 17K05355. Publisher Copyright: {\textcopyright} 2018, The Author(s).",
year = "2019",
month = mar,
day = "15",
doi = "10.1007/s10884-018-9694-7",
language = "English",
volume = "31",
pages = "153--203",
journal = "Journal of Dynamics and Differential Equations",
issn = "1040-7294",
publisher = "Springer New York",
number = "1",
}