| [1] |
Engel, T., A molecular beam investigation of He, CO, and \(\operatorname{O}_2\) scattering from Pd(111), J. Chem. Phys., 69, 373, 1978 · doi:10.1063/1.436363 |
| [2] |
Engel, T.; Ertl, G., Elementary steps in the catalytic oxidation of carbon monoxide on platinum metals, Adv. Catal., 28, 1-78, 1979 · doi:10.1016/S0360-0564(08)60133-9 |
| [3] |
Ertl, G.; Norton, P. R.; Rüstig, J., Kinetic oscillations in the platinum-catalyzed oxidation of CO, Phys. Rev. Lett., 49, 177-180, 1982 · doi:10.1103/PhysRevLett.49.177 |
| [4] |
Krischer, K.; Eiswirth, M.; Ertl, G., Bifurcation analysis of an oscillating surface reaction model, Surf. Sci., 251-252, 900-904, 1991 · doi:10.1016/0039-6028(91)91121-D |
| [5] |
Falcke, M.; Bär, M.; Engel, H.; Eiswirth, R. M., Traveling waves in the CO oxidation on Pt(110): Theory, J. Chem. Phys., 97, 4555-4563, 1992 · doi:10.1063/1.463900 |
| [6] |
Nettesheim, S.; Rotermund, H. H.; Ertl, G., Reaction diffusion patterns in the catalytic propagation on Pt(100): Front propagation and spiral waves, J. Chem. Phys., 98, 9977-9985, 1993 · doi:10.1063/1.464323 |
| [7] |
Méndez, V., Fedotov, S., and Horsthemke, W., Reaction-Transport Systems, Springer Series in Synergetics (Springer, Berlin, 2010). |
| [8] |
Clerc, M. G.; Elías, R. G.; Rojas, R. G., Continuous description of lattice discreteness effects in front propagation, Philos. Trans. R. Soc. A, 369, 412-424, 2011 · Zbl 1211.82034 · doi:10.1098/rsta.2010.0255 |
| [9] |
Cisternas, J.; Rohe, K.; Wehner, S., Reaction-diffusion fronts and the butterfly set, Chaos, 30, 113138, 2020 · Zbl 1458.35104 · doi:10.1063/5.0022298 |
| [10] |
Stegemerten, F.; Gurevich, S.; Thiele, U., Bifurcations of front motion in passive and active Allen-Cahn-type equations, Chaos, 30, 053136, 2020 · Zbl 1445.35039 · doi:10.1063/5.0003271 |
| [11] |
Ambrosio, B.; Aziz-Alaoui, M., Synchronization and control of coupled reaction-diffusion systems of the FitzHugh-Nagumo type, Comput. Math., 64, 934-943, 2012 · Zbl 1356.93039 · doi:10.1016/j.camwa.2012.01.056 |
| [12] |
Khatibi, S., Cassol, G. O., and Dubljevic, S., “Linear model predictive control for a cascade ODE-PDE system,” in 2020 American Control Conference (ACC) (IEEE, Denver, CO, 2020), pp. 4521-4526. |
| [13] |
Stamatakis, M.; Chen, Y.; Vlachos, D. G., First-principles-based kinetic Monte Carlo simulation of the structure sensitivity of the water-gas shift reaction on platinum surfaces, J. Phys. Chem. C, 115, 24750-24762, 2011 · doi:10.1021/jp2071869 |
| [14] |
Eiswirth, M.; Möller, P.; Wetzl, K.; Imbihl, R.; Ertl, G., Mechanisms of spatial self-organization in isothermal kinetic oscillations during the catalytic CO oxidation on Pt single crystal surfaces, J. Chem. Phys., 90, 510-521, 1989 · doi:10.1063/1.456501 |
| [15] |
Wehner, S.; Hoffmann, P.; Schmeisser, D.; Brand, H. R.; Küppers, J., The consequences of anisotropic diffusion and noise: PEEM at the CO oxidation reaction on stepped Ir(111) surfaces, Chem. Phys. Lett., 423, 39-44, 2006 · doi:10.1016/j.cplett.2006.03.010 |
| [16] |
Wehner, S.; Hoffmann, P.; Schmeisser, D.; Brand, H. R.; Küppers, J., Influence of the substrate on the pattern formation of a surface reaction, AIP Conf. Proc., 913, 121-126, 2007 · doi:10.1063/1.2746735 |
| [17] |
Peyrard, M.; Kruskal, M. D., Kink dynamics in the highly discrete sine-Gordon system, Physica D, 14, 88-102, 1984 · doi:10.1016/0167-2789(84)90006-X |
| [18] |
Keener, J. P., Propagation and its failure in coupled systems of discrete excitable cells, SIAM J. Appl. Math., 47, 556-572, 1987 · Zbl 0649.34019 · doi:10.1137/0147038 |
| [19] |
Laplante, J. P.; Erneux, T., Propagation failure in arrays of coupled bistable chemical reactors, J. Phys. Chem., 96, 4931-4934, 1992 · doi:10.1021/j100191a038 |
| [20] |
Erneux, T.; Nicolis, G., Propagating waves in discrete bistable reaction-diffusion systems, Physica D, 67, 237-244, 1993 · Zbl 0787.92010 · doi:10.1016/0167-2789(93)90208-I |
| [21] |
Booth, V.; Erneux, T.; Laplante, J.-P., Experimental and numerical study of weakly coupled bistable chemical reactors, J. Phys. Chem., 98, 6537-6540, 1994 · doi:10.1021/j100077a019 |
| [22] |
Woods, P.; Champneys, A., Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation, Physica D, 129, 147-170, 1999 · Zbl 0952.37009 · doi:10.1016/S0167-2789(98)00309-1 |
| [23] |
Taylor, C.; Dawes, J. H., Snaking and isolas of localised states in bistable discrete lattices, Phys. Lett. A, 375, 14-22, 2010 · Zbl 1241.35201 · doi:10.1016/j.physleta.2010.10.010 |
| [24] |
Seidel, T.; Perego, A.; Javaloyes, J.; Gurevich, S., Discrete light bullets in passively mode-locked semiconductor lasers, Chaos, 30, 063102, 2020 · doi:10.1063/5.0002989 |
| [25] |
Humphries, A. R. and Wilds, R. P., “Traveling wave solutions of lattice differential equations through an embedding approach,” (2006); available at http://www.math.mcgill.ca/humphries/research/papers/ETWANMSub081206.pdf. |
| [26] |
Qi, H.; Li, Z.-C.; Wang, S.-M.; Wu, L.; Xu, F.; Liu, Z.-L.; Li, X.; Wang, J.-Z., Tristability in mitochondrial permeability transition pore opening, Chaos, 31, 123108, 2021 · doi:10.1063/5.0065400 |
| [27] |
Huang, B.; Xia, Y.; Liu, F.; Wang, W., Realization of tristability in a multiplicatively coupled dual-loop genetic network, Sci. Rep., 6, 28096, 2016 · doi:10.1038/srep28096 |
| [28] |
De Mot, L.; Gonze, D.; Bessonnard, S.; Chazaud, C.; Goldbeter, A.; Dupont, G., Cell fate specification based on tristability in the inner cell mass of mouse blastocysts, Biophys. J., 110, 710-722, 2016 · doi:10.1016/j.bpj.2015.12.020 |
| [29] |
Poston, T. and Stewart, I., “The first seven catastrophe geometries,” in Catastrophe Theory and Its Applications (Dover Publications, Mineola, NY, 1996). |
| [30] |
Pazó, D.; Deza, R. R.; Pérez-Muñuzuri, V., Parity-breaking front bifurcation in bistable media: Link between discrete and continuous versions, Phys. Lett. A, 340, 132-138, 2005 · Zbl 1145.37341 · doi:10.1016/j.physleta.2005.03.026 |
| [31] |
Van Vleck, E. S.; Mallet-Paret, J.; Cahn, J. W., Traveling wave solutions for systems of ODEs on a two-dimensional spatial lattice, SIAM J. Appl. Math., 59, 455-493, 1998 · Zbl 0917.34052 · doi:10.1137/S0036139996312703 |
| [32] |
Hupkes, H. J., Morelli, L., Schouten-Straatman, W. M., and Van Vleck, E. S., “Traveling waves and pattern formation for spatially discrete bistable reaction-diffusion equations,” in Difference Equations and Discrete Dynamical Systems with Applications, edited by M. Bohner, S. Siegmund, R. Šimon Hilscher, and P. Stehlík (Springer International Publishing, 2020), Vol. 312, pp. 55-112. · Zbl 1447.34001 |
| [33] |
Patra, M.; Karttunen, M., Stencils with isotropic discretization error for differential operators, Numer. Methods Partial Differ. Equ., 22, 936-953, 2006 · Zbl 1098.65108 · doi:10.1002/num.20129 |
| [34] |
Bechhoefer, J.; Löwen, H.; Tuckerman, L. S., Dynamical mechanism for the formation of metastable phases, Phys. Rev. Lett., 67, 1266-1269, 1991 · doi:10.1103/PhysRevLett.67.1266 |
| [35] |
Rubinstein, J.; Sternberg, P.; Keller, J. B., Front interaction and nonhomogeneous equilibria for tristable reaction-diffusion equations, SIAM J. Appl. Math., 53, 1669-1685, 1993 · Zbl 0806.35081 · doi:10.1137/0153077 |
| [36] |
Hupkes, H. J.; Pelinovsky, D.; Sandstede, B., Propagation failure in the discrete Nagumo equation, Proc. Am. Math. Soc., 139, 3537, 2011 · Zbl 1235.34034 · doi:10.1090/S0002-9939-2011-10757-3 |
| [37] |
Doedel, E., “AUTO-07P: Continuation and bifurcation software for ordinary differential equations,” Technical Report, Concordia University, Montreal, QC, 2007. |
| [38] |
Balmforth, N.; Craster, R.; Kevrekidis, P., Being stable and discrete, Physica D, 135, 212-232, 2000 · Zbl 0936.35168 · doi:10.1016/S0167-2789(99)00137-2 |
| [39] |
Martsenyuk, V.; Veselska, O., On nonlinear reaction-diffusion model with time delay on hexagonal lattice, Symmetry, 11, 758, 2019 · doi:10.3390/sym11060758 |
| [40] |
Harris, C. R.; Millman, K. J.; van der Walt, S. J.; Gommers, R.; Virtanen, P.; Cournapeau, D.; Wieser, E.; Taylor, J.; Berg, S.; Smith, N. J.; Kern, R.; Picus, M.; Hoyer, S.; van Kerkwijk, M. H.; Brett, M.; Haldane, A.; del Río, J. F.; Wiebe, M.; Peterson, P.; Gérard-Marchant, P.; Sheppard, K.; Reddy, T.; Weckesser, W.; Abbasi, H.; Gohlke, C.; Oliphant, T. E., Array programming with NumPy, Nature, 585, 357-362, 2020 · doi:10.1038/s41586-020-2649-2 |
| [41] |
Virtanen, P.; Gommers, R.; Oliphant, T. E.; Haberland, M.; Reddy, T.; Cournapeau, D.; Burovski, E.; Peterson, P.; Weckesser, W.; Bright, J.; van der Walt, S. J.; Brett, M.; Wilson, J.; Millman, K. J.; Mayorov, N.; Nelson, A. R. J.; Jones, E.; Kern, R.; Larson, E.; Carey, C. J.; Polat, İ.; Feng, Y.; Moore, E. W.; VanderPlas, J.; Laxalde, D.; Perktold, J.; Cimrman, R.; Henriksen, I.; Quintero, E. A.; Harris, C. R.; Archibald, A. M.; Ribeiro, A. H.; Pedregosa, F.; van Mulbregt, P., SciPy 1.0: Fundamental algorithms for scientific computing in Python, Nat. Methods, 17, 261-272, 2020 · doi:10.1038/s41592-019-0686-2 |
| [42] |
Lam, S. K., Pitrou, A., and Seibert, S., “Numba: A LLVM-based Python JIT compiler,” in LLVM’15: Proceedings of the Second Workshop on the LLVM Compiler Infrastructure in HPC (Association for Computing Machinery, New York, 2015). |
| [43] |
Hunter, J. D., Matplotlib: A 2D graphics environment, Comput. Sci. Eng., 9, 90-95, 2007 · doi:10.1109/MCSE.2007.55 |
