References
- S. Brown, J. Dockery, and M. Pernarowski, Traveling wave solutions of a reaction diffusion model for competing pioneer and climax species, Math. Biosci. 194 (2005), pp. 21–36.
- J. Buchanan, Asymptotic behavior of two interacting pioneer-climax species, Fields Inst. Commun.21 (1999), pp. 51–63.
- J. Buchanan, Turing instability in pioneer/climax species interactions, Math. Biosci. 194 (2005), pp. 199–216.
- J. Cao and P. Weng, Single spreading speed and traveling wave solutions of a diffusive pioneer-climax model without cooperative property, Comm. Pur. Appl. Anal. 16 (2017), pp. 1405–1426.
- W. Ding, X. Liang, and B. Xu, Spreading speeds of N-season spatially periodic integro-difference models, Disc. Cont. Dyn. Syst. 33 (2013), pp. 3443–3472.
- J.E. Franke and A-A. Yakubu, Pioneer exclusion in a one-hump discrete pioneer-climax competitive system, J. Math. Biol. 32 (1994), pp. 771–787.
- N.M. Gilbertson and M. Kot, Dynamics of a discrete-time pioneer-climax model, Theor. Ecol. 14 (2021), pp. 501–523.
- S.B. Hsu and X.Q. Zhao, Spreading speeds and traveling waves for nonmonotone integrodifference equations, SIAM J. Math. Anal. 40 (2008), pp. 776–789.
- Y. Huang and P. Weng, Traveling wavefronts of a diffusive competing pioneer and climax system with delays, Math. Comput. Model. 57 (2013), pp. 2532–2548.
- M. Kot, Discrete-time travelling waves: ecological examples, J. Math. Biol. 30 (1992), pp. 413–436.
- M. Kot and W.M. Schaffer, Discrete-time growth-dispersal models, Math. Biosci. 80 (1986), pp. 109–136.
- B.T. Li, H.F. Weinberger, and M.A. Lewis, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci. 196 (2005), pp. 82–98.
- X. Liang and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Commun. Pure Appl. Math. 60 (2007), pp. 1–40.
- G. Lin, Traveling wave solutions for integro-difference systems, J. Diff. Eqns. 258 (2015), pp. 2908–2940.
- G. Lin, W.-T. Li, and S. Ruan, Spreading speeds and traveling waves in competitive recursion systems, J. Math. Biol. 62 (2011), pp. 165–201.
- R. Lui, Biological growth and spread modeled by systems of recursions. I. mathematical theory, Math. Biosci. 93 (1989), pp. 269–295.
- F. Lutscher, Density-dependent dispersal in integrodifference equations, J. Math. Biol. 56 (2008), pp. 499–524.
- F. Lutscher, Integrodifference Equations in Spatial Ecology, Springer, New York, 2019.
- M. Ma and C. Ou, Linear and nonlinear speed selection for mono-stable wave propagations, SIAM J. Math. Anal. 51 (2019), pp. 321–345.
- J.F. Selgrade and G. Namkoong, Stable periodic behavior in a pioneer-climax model, Nat. Resour. Model. 4 (1990), pp. 215–227.
- S. Sumner, Stable periodic behavior in pioneer-climax competing species models with constant rate forcing, Nat. Resour. Model. 11 (1998), pp. 155–171.
- H. Wang and C. Castillo-Chavez, Spreading speeds and traveling waves for non-cooperative integro-difference systems, Disc. Cont. Dyn. Syst. Ser. B. 17 (2012), pp. 2243–2266.
- H.F. Weinberger, K. Kawasaki, and N. Shigesada, Spreading speeds of spatially periodic integro-difference models for populations with nonmonotone recruitment functions, J. Math. Biol. 57 (2008), pp. 387–411.
- H.F. Weinberger, M.A. Lewis, and B.T. Li, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol. 45 (2002), pp. 183–218.
- H.F. Weinberger, M.A. Lewis, and B. Li, Anomalous spreading speeds of cooperative recursion systems, J. Math. Biol. 55 (2007), pp. 207–222.
- P. Weng and X. Zou, Minimal wave speed and spread speed of competing pioneer and climax species, Appl. Anal. 93 (2014), pp. 2093–2110.
- R. Wu and X.-Q. Zhao, Propagation dynamics for a spatially periodic integrodifference competition model, J. Diff. Eqns. 264 (2018), pp. 6507–6534.
- X. Yu, P. Weng, and Y. Huang, Traveling wavefronts of competing pioneer and climax model with nonlocal diffusion, Abstr. Appl. Anal. 2013 (2013), Article id 725495, pp. 1–12.
- Z. Yuan and X. Zou, Co-invasion waves in a reaction diffusion model for competing pioneer and climax species, Nonlinear Anal. RWA 11 (2010), pp. 232–245.
- Y. Zhang and S. Ma, Invasion dynamics of a diffusive pioneer-climax model: monotone and non-monotone cases, Disc. Cont. Dyn. Syst. Ser. B. 26 (2021), pp. 4767–4788.
- Y. Zhang and X.-Q. Zhao, Bistable travelling waves in competitive recursion systems, J. Diff. Eqns.252 (2012), pp. 2630–2647.