The Number of Isolated Periodic Traveling Waves in a Class of Single Species Model

• Guiyan Kou ^[1] ; Yangjian Sun ^[1] ; Qing Ge ^[2]
  1. [1] Shangrao Normal University

     Shangrao Normal University

     China

     
  2. [2] Guilin University of Electronic Technology

     Guilin University of Electronic Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 4, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper is dedicated to considering global isolated periodic traveling waves in a single population model described by a reaction-diffusion equation. From the corresponding planar traveling wave system, we use the Chebyshev criterion and prove that the maximum number of isolated periodic waves is 2 and can be reached.

• Referencias bibliográficas
  • 1. Arnold, V.I.: Geometrical Methods in the Theory of Ordinary Differential Equations. Springer-Verlag (1983)
  • 2. Allee, W.C.: Animal Aggregations. University of Chicago Press, Chicago (1931)
  • 3. Dumortier, F., Li, C.: Perturbations from an elliptic Hamiltonian of degree four: (I) saddle loop and two saddle cycle. J. Differ. Equ....
  • 4. Ji, G., Liu, C., Li, P.: Bifurcation of limit cycles for a perturbed piecewise quadratic diferential systems. Acta Math. Sin. 38(3), 591–611...
  • 5. Mañosas, F., Villadelprat, J.: Bounding the number of zeros of certain Abelian integrals. J. Differ. Equ. 251, 1656–1669 (2011)
  • 6. Grau, M., Mañosas, F., Villadelprat, J.: A Chebyshev criterion for Abelian integrals. Trans. Am. Math. Soc. 363, 109–129 (2011)
  • 7. Liu, C., Xiao, D.: The monotonicity of the ratio of two Abelian integrals. Trans. Am. Math. Soc. 365, 5525–5544 (2013)
  • 8. Liu, C., Xiao, D.: The lowest upper bound on the number of zeros of Abelian integrals. J. Differ. Equ. 269, 3816–3852 (2020)
  • 9. Li, C., Zhang, Z.: A criterion for determining the monotonocity of the ratio of two Abelian integrals. J. Differ. Equ. 124, 407–424 (1996)
  • 10. M.A. Lewis, S.V. Petrovskii, J.R. Potts, The Mathematics Behind Biological Invasions, Springer International Publishing, (2016)
  • 11. Petrovskii, S.V., Li, B.L.: An exactly solvable model of population dynamics with density-dependent migrations and the Allee effect. Math....
  • 12. Sun, X., Yu, P., Qin, B.: Global existence and uniqueness of periodic waves in a population model with density dependent migrations and...
  • 13. Wang, Q., Huang, W.: Limit periodic travelling wave solution of a model for biological invasions. Appl. Math. Lett. 34, 13–16 (2014)
  • 14. Wang, Q., Xiong, Y., Huang, W., Yu, P.: Isolated periodic wave solutions arising from Hopf and Poincaré bifurcations in a class of single...