Traveling wave solutions for three-species nonlocal competitive-cooperative systems
DOI:
https://doi.org/10.58997/ejde.2023.55Abstract
By using a two-point boundary-value problem and a Schauder's fixed point theorem, we obtain traveling wave solutions connecting \((0,0,0)\) to an unknown positive steady state for speed \(c\geq c^{\ast}=\max\{2,2\sqrt{d_2r_2},2\sqrt{d_3r_3}\}\). Then we present some asymptotic behaviors of traveling wave solutions. In particular we show that the nonlocal effects have a great influence on the final state of traveling wave solutions at \(-\infty\).
For more information see https://ejde.math.txstate.edu/Volumes/2023/55/abstr.html
References
C.-H. Chang, C.-C. Chen, L.-C. Hung, M. Mimura, T. Ogawa; Existence and stability of nonmonotone travelling wave solutions for the diffusive Lotka-Volterra system of three competing species, Nonlinearity 33 (2020), no. 10, 5080-5110.
F.-D. Dong, W.-T. Li, J.-B. Wang; Propagation dynamics in a three-species competition model with nonlocal anisotropic dispersal, Nonlinear Anal. Real World Appl. 48 (2019), 232-266.
J. Fang, J.-H.Wu; Monotone traveling waves for delayed Lotka-Volterra competition systems, Discrete Contin. Dyn. Syst. 32 (2012), no. 9, 3043-3058.
J.-S. Guo, X. Liang; The minimal speed of traveling fronts for the Lotka-Volterra competition system, J. Dynam. Differential Equations 23 (2011), no. 2, 353-363.
J.-S. Guo, C.-H. Wu; Recent developments on wave propagation in 2-species competition systems, Discrete Contin. Dyn. Syst. Ser. B 17 (2012), no. 8, 2713-2724.
B.-S. Han, Z.-C. Wang, Z.-J. Du; Traveling Waves for Nonlocal Lotka-Volterra Competition Systems, Discrete Contin. Dyn. Syst. Ser. B 25 (2020), no. 5, 1959-1983.
B.-S. Han, Z. Feng, W.-J. Bo; Traveling wave phenomena of a nonlocal reaction-diffusion equation with degenerate nonlinearity. Commun. Nonlinear Sci. Numer. Simul. 103 (2021), Paper No. 105990, 21 pp.
B.-S. Han, D.-Y. Kong; Propagation dynamics of a nonlocal reaction-diffusion system, Discrete Contin. Dyn. Syst. 43 (2023) 2756-2780.
Y.-C. Hao, G.-B. Zhang; Stability of bistable traveling wavefronts for a nonlocal dispersal epidemic system, Electron. J. Differential Equations 2022 (2022), no. 49, 1-21.
J.-H. Huang, X.-F. Zou; Traveling wavefronts in diffusive and cooperative Lotka-Volterra system with delays, J. Math. Anal. Appl. 271 (2002), no. 2, 455-466.
J.-H. Huang, X.-F. Zou; Existence of traveling wavefronts of delayed reaction diffusion systems without monotonicity, Discrete Contin. Dyn. Syst. 9 (2003), no. 4, 925-936.
L.-C. Hung; Traveling wave solutions of competitive-cooperative Lotka-Volterra systems of three species, Nonlinear Anal. Real World Appl. 12 (2011), no. 6, 3691-3700.
X.-J. Hou, A. W. Leung; Traveling wave solutions for a competitive reaction-diffusion system and their asymptotics, Nonlinear Anal. Real World Appl. 9 (2008), no. 5, 2196-2213.
A. W. Leung, X.-J. Hou, Y. Li; Exclusive traveling waves for competitive reaction-diffusion systems and their stabilities, J. Math. Anal. Appl. 338 (2008), no. 2, 902-924.
G.-Y. Lv, M.-X. Wang; Traveling wave front in diffusive and competitive Lotka-Volterra system with delays, Nonlinear Anal. Real World Appl. 11 (2010), no. 3, 1323-1329.
K. Li, X. Li; Traveling wave solutions in a delayed diffusive competition system, Nonlinear Anal. 75 (2012), no. 9, 37053722.
G.-C. Lu, Z.-Y. Lu; Geometric approach for global asymptotic stability for three species competitive Gompertz models, J. Math. Anal. Appl. 445 (2017), no. 1, 13-22.
W.-T. Li, G. Lin, S. Ruan; Existence of travelling wave solutions in delayed reaction-diffusion systems with applications to diffusion-competition systems, Nonlinearity. 19 (2006), no. 6, 1253-1273.
S.-W. Ma; Traveling wavefronts for delayed reaction-diffusion systems via a fixed point theorem, J. Differential Equations. 171 (2001), no. 2, 294-314.
Y.-L. Meng, W.-G. Zhang; Properties of traveling wave fronts for three species Lotka-Volterra system, Qual. Theory Dyn. Syst. 19 (2020), no. 2, Paper No. 67, 28 pp.
Z.-H. Ma, X. Wu, R. Yuan; Nonlinear stability of traveling wavefronts for competitivecooperative Lotka-Volterra systems of three species, Appl. Math. Comput. 315 (2017) 331-346.
Q. Liu, S. Liu, K. Y. Lam; Stacked invasion waves in a competition-diffusion model with three species, J. Differential Equations 271 (2021), 665-718.
Y.-L. Tian, X.-Q. Zhao; Bistable traveling waves for a competitive-cooperative system with nonlocal delays, J. Differential Equations 264 (2018), no. 8, 5263-5299.
C.-Y. Wang, L.-R. Li, Q.-Y. Zhang, R. Li; Dynamical behaviour of a Lotka-Volterra competitive-competitive-cooperative model with feedback controls and time delays, J. Biol. Dyn. 13 (2019), no. 1, 43-68.
J.-H. Wu, X.-F. Zou; Traveling wave fronts of reaction-diffusion systems with delay, J. Dynam. Differential Equations 13 (2001), no. 3, 651-687.
L. Zhang, X.-X. Bao; Propagation dynamics of a three-species nonlocal competitivecooperative system, Nonlinear Anal. Real World Appl. 58 (2021), 103230, 17 pp.
H. Zhao, S.-L.Wu; Regular traveling waves for a reaction-diffusion equation with two nonlocal delays, Electron. J. Differential Equations 2022 (2022), no. 82, 1-16.
Y. Zhao, S.-L. Yuan, J.-L. Ma; Survival and stationary distribution analysis of a stochastic competitive model of three species in a polluted environment, Bull. Math. Biol. 77 (2015), no. 7, 1285-1326.
X.-F. Zou, J.-H. Wu; Existence of traveling wave fronts in delayed reaction-diffusion systems via the monotone iteration method, Proc. Amer. Math. Soc. 125 (1997), no. 9, 2589-2598.
W.-J. Zuo, D.-Q. Jiang, X.-G. Sun, T. Hayat, A. Alsaedi; Long-time behaviors of a stochastic cooperative Lotka-Volterra system with distributed delay, Phys. A 506 (2018), 542-559.
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Copyright (c) 2023 Hong-Jie Wu, Bang-Sheng Han, Shao-Yue Mi, Liang-Bin Shen
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