Long Time Behavior for Time-Periodic Lotka-Volterra Competition System with Nonlocal Dispersal

• Liyan Pang ^[1] ; Xiao Zhang ^[2]
  1. [1] Xianyang Normal University

     Xianyang Normal University

     China

     
  2. [2] Xidian University

     Xidian University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 6, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper is concerned with the long time behavior of solutions to a time-periodic Lotka-Volterra strong competition system with nonlocal dispersal when the two species are initially absent from the right half-line x ≥ 0 and the slower one dominates the faster one on x < 0. Due to the presence of the time-periodicity, the long time behavior relies on the construction of nontrivial super- and subsolutions and establishment the exponential decay of critical periodic traveling waves for a time-periodic nonlocal dispersal equation.

• Referencias bibliográficas
  • 1. Bao, X., Wang, Z.-C.: Existence and stability of time periodic traveling waves for a periodic bistable Lotka-Volterra competition system....
  • 2. Bo, W.-J., Lin, G., Ruan, S.: Traveling wave solutions for time periodic reaction-diffusion systems. Discrete Contin. Dyn. Syst. 38, 4329–4351...
  • 3. Carrère, C.: Spreading speeds for a two-species competition-diffusion system. J. Differential Equations 264, 2133–2156 (2018)
  • 4. Chasseigne, E., Chaves, M., Rossi, J.D.: Asymptotic behavior for nonlocal diffusion equations. J. Math. Pures Appl. 86, 271–291 (2006)
  • 5. Ding, W., Matano, H.: Dynamics of time-periodic reaction-diffusion equations with front-like initial data on R. SIAM J. Math. Anal. 52,...
  • 6. Ducrot, A., Giletti, T., Matano, H.: Existence and convergence to a propagating terrace in one dimensional reaction-diffusion equations....
  • 7. Fife, P., McLeod, J.: The approach of solutions of nonlinear diffusion equations to travelling front solutions. Arch. Ration. Mech. Anal....
  • 8. Garcia-Melian, J., Rossi, J.: On the principal eigenvalue of some nonlocal diffusion problems. J. Differential Equations 246, 21–38 (2009)
  • 9. Hsu, S.-B., Wang, F.-B., Zhao, X.-Q.: Dynamics of a periodically pulsed bio-reactor model with a hydraulic storage zone. J. Dynam. Differential...
  • 10. Jin, Y., Zhao, X.-Q.: Spatial dynamics of a periodic population model with dispersal. Nonlinearity 22, 1167–1189 (2009)
  • 11. Liang, X., Yi, Y., Zhao, X.-Q.: Spreading speeds and traveling waves for periodic evolution system. J. Differential Equations 231, 57–77...
  • 12. Nguyen, T., Rawal, N.: Coexistence and extinction in time-periodic Volterra-Lotka type systems with nonlocal dispersal. Discrete Contin....
  • 13. Pang, L., Wu, S.-L.: Time-periodic traveling waves for a periodic Lotka-Volterra competition system with nonlocal dispersal. Commun. Nonlinear...
  • 14. Pang, L., Wu, S.-L., Ruan, S.: Long time behavior for a periodic Lotka-Volterra reaction- diffusion system with strong competition. Calc....
  • 15. Poláˇcik, P.: Planar propagating terraces and the asymptotic one-dimensional symmetry of solutions of semilinear parabolic equations....
  • 16. Poláˇcik, P.: Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on R, Mem. Amer. Math. Soc.,...
  • 17. Wang, Z.-C., Zhang, L., Zhao, X.-Q.: Time periodic traveling waves for a periodic and diffusive SIR epidemic model. J. Dynam. Differential...
  • 18. Wu, S.-L., Hsu, C.-H.: Periodic traveling fronts for partially degenerate reaction-diffusion systems with bistable and time-periodic nonlinearity....
  • 19. Wu, S.-L., Pang, L., Ruan, S.: Propagation dynamics in periodic predator-prey systems with nonlocal dispersal. J. Math. Pures Appl. 170,...
  • 20. Zhang, G.-B., Zhao, X.-Q.: Propagation phenomena for a two-species Lotka-Volterra strong competition system with nonlocal dispersal. Calc....
  • 21. Zhao, G., Ruan, S.: Existence, uniqueness and asymptotic stability of time periodic traveling waves for a periodic Lotka-Volterra competition...
  • 22. Zhao, G., Ruan, S.: Time periodic traveling wave solutions for periodic advection-reaction-diffusion systems. J. Differential Equations...