1Alfaro, M. and Coville, J.. Rapid traveling waves in the nonlocal fisher equation connect two unstable states. Appl. Math. Lett. 25 (2012), 2095–2099.
2Alfaro, M., Coville, J. and Raoul, G.. Travelling waves in a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypic trait. Commun. Partial Differ. Equ. 38 (2013), 2126–2154.
3Arnold, A., Desvillettes, L. and Prévost, C.. Existence of nontrivial steady states for populations structured with respect to space and a continuous trait. Commun. Pure Appl. Anal. 11 (2012), 83–96.
4Bénichou, O., Calvez, V., Meunier, N. and Voituriez, R.. Front acceleration by dynamic selection in fisher population waves. Phys. Rev. E 86 (2012), 041908.
5Berestycki, H., Nadin, G., Perthame, B. and Ryzhik, L.. The non-local Fisher–KPP equation: travelling waves and steady states. Nonlinearity 22 (2009), 2813.
6Bouin, E. and Calvez, V.. Travelling waves for the cane toads equation with bounded traits. Nonlinearity 27 (2014), 2233–2253.
7Bouin, E., Calvez, V., Meunier, N., Mirrahimi, S., Perthame, B., Raoul, G. and Voituriez, R.. Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration. Comptes Rendus Mathematique 350 (2012), 761–766.
8Bouin, E., Henderson, C. and Ryzhik, L.. , (2015).
9Cantrell, R. S., Cosner, C. and Yu, X.. Dynamics of populations with individual variation in dispersal on bounded domains. J. Biol. Dyn. 12 (2018), 288–317.
10Ducrot, A., Giletti, T. and Matano, H.. Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations. Trans. Amer. Math. Soc. 366 (2014), 5541–5566.
11Eaton, J. W., Bateman, D., Hauberg, S. and Wehbring, R.. , (2019).
12Elliott, E. C. and Cornell, S. J.. Dispersal polymorphism and the speed of biological invasions. PLOS ONE 7 (2012), 1–10, 07.
13Faye, G. and Holzer, M.. Modulated traveling fronts for a nonlocal fisher-kpp equation: a dynamical systems approach. J. Differ. Equ. 258 (2015), 2257–2289.
14Fife, P. C.. Mathematical aspects of reacting and diffusing systems, (Berlin-New York: Springer-Verlag, 1979).
15Fraile, J. M. and Sabina, J.. Kinetic conditions for the existence of wave fronts in reaction-diffusion systems. Proc. Roy. Soc. Edinburgh Sect. A 103 (1986), 161–177.
16Fraile, J. M. and Sabina, J. C.. General conditions for the existence of a ‘critical point-periodic wave front’ connection for reaction-diffusion systems. Nonlinear Anal. 13 (1989), 767–786.
17Girardin, L.. Non-cooperative Fisher–KPP systems: Asymptotic behavior of traveling waves. Math. Models Methods Appl. Sci. 28 (2018), 1067–1104.
18Girardin, L.. Non-cooperative Fisher–KPP systems: traveling waves and long-time behavior. Nonlinearity 31 (2018), 108.
19Griette, Q. and Raoul, G.. Existence and qualitative properties of travelling waves for an epidemiological model with mutations. J. Differ. Equ. 260 (2016), 7115–7151.
20Horn, R. A. and Johnson, C. R.. Topics in Matrix Analysis (Cambridge: Cambridge University Press, 1991).
21Kopell, N. and Howard, L. N.. Plane wave solutions to reaction-diffusion equations. Studies in Appl. Mat. 52 (1973), 291–328.
22Kuznetsov, Y. A.. Elements of Applied Bifurcation Theory, , 3rd edn (New York: Springer-Verlag, 2004).
23Maginu, K.. Stability of spatially homogeneous periodic solutions of reaction-diffusion equations. J. Differ. Equ. 31 (1979), 130–138.
24Maginu, K.. Stability of periodic travelling wave solutions with large spatial periods in reaction-diffusion systems. J. Differ. Equ. 39 (1981), 73–99.
25May, R. M. and Leonard, W. J.. Nonlinear aspects of competition between three species. SIAM J. Appl. Math. 29 (1975), 243–253..
26Morris, A., Börger, L. and Crooks, E. C. M.. , dec 2016.
27Murray, J. D.. Mathematical Biology. II, , 3rd edn (New York: Springer-Verlag, 2003), .
28Nadin, G.. Traveling fronts in space-time periodic media. J. Math. Pures Appl. (9) 92 (2009), 232–262.
29Nadin, G., Perthame, B. and Tang, M.. Can a traveling wave connect two unstable states?: The case of the nonlocal Fisher equation. C. R. Math. Acad. Sci. Paris 349 (2011), 553–557.
30Petrovskii, S., Kawasaki, K., Takasu, F. and Shigesada, N.. Diffusive waves, dynamical stabilization and spatio-temporal chaos in a community of three competitive species. Japan J. Indust. Appl. Math. 18 (2001), 459–481..
31Prévost, C.. , (2004).
32Sherratt, J. A.. Invading wave fronts and their oscillatory wakes are linked by a modulated travelling phase resetting wave. Phys. D 117 (1998), 145–166.
33Smith, M. J. and Sherratt, J. A.. The effects of unequal diffusion coefficients on periodic travelling waves in oscillatory reaction-diffusion systems. Phys. D 236 (2007), 90–103.
34Uno, T. and Odani, K.. , pp. 1405–1410, (1997).
35Zeeman, M.-L.. Hopf bifurcations in competitive three-dimensional Lotka–Volterra systems. Dynam. Stability Systems 8 (1993), 189–217.