Existence of Positive Periodic Solutions for a Neutral Delay Predator–Prey Model with Hassell–Varley Type Functional Response and Impulse

• Chen, Xiao ^[1] ; Du, Zengji ^[1]
  1. [1] Jiangsu Normal University

     Jiangsu Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 1, 2018, págs. 67-80
• Idioma: inglés
• DOI: 10.1007/s12346-017-0223-6
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we discuss a neutral delay predator–prey model with Hassel–Varley type functional response and impulse is investigated. By using Mawhin coincidence degree theory, we obtain some sufficient conditions for the existence of positive periodic solutions. We extend some known work.

• Referencias bibliográficas
  • 1. Hassell, M., Varley, G.: New inductive population model for insect parasites and its bearing on biological control. Nature 223, 1133–1136...
  • 2. Wang, K.: Periodic solutions to a delayed predator-prey model with Hassell–Varley type functional response. Nonlinear Anal. Real World...
  • 3. Kuang, Y.: On neutral delay logistic Gauss-type predator-prey systems. Dyn. Stab. Syst. 6, 173–189 (1991)
  • 4. Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, Boston (1993)
  • 5. Zhang, F., Zheng, C.: Positive periodic solutions for the neutral ratio-dependent predator–prey model. Comput. Math. Appl. 61, 2221–2226...
  • 6. Samoikleno, A.M., Perestyuk, N.A.: Impulsive Differential Equations. World Scientific, Singapore (1995)
  • 7. Zavalishchhin, S.T., Sesekin, A.N.: Dynamic Impulse Systems, Theory and Applications. Kluwer Academic Publishers Group, Dordrecht (1997)
  • 8. Huo, H.: Existence of positive periodic solutions of a neutral delay Lotka–Volterra system with impulses. Comput. Math. Appl. 48, 1833–1846...
  • 9. Dai, B., Su, H., Hu, D.: Periodic Solution of a delayed ratio-dependent predator–prey model with monotonic functional response and impulse....
  • 10. Wang, Q., Dai, B.: Existence of positive periodic solutions for a neutral population model with delays and impulse. Nonlinear Anal. 69,...
  • 11. Du, Z., Feng, Z.: Periodic solutions of a neutral impulsive predator–prey model with Beddington– DeAngelis functional response with delays....
  • 12. Lv, Y., Du, Z.: Existence and global attractivity of a positive periodic solution to a Lotka–Volterra model with mutual interference and...
  • 13. Du, Z., Lv, Y.: Permanence and almost periodic solution of a Lotka–Volterra model with mutual interference and time delays. Appl. Math....
  • 14. Terry, A.J.: Predator–prey models with component Allee effect for predator reproduction. J. Math. Biol. 71, 1325–1352 (2015)
  • 15. Ducrot, A., Langlais, M.: A singular reaction–diffusion system modelling prey–predator interactions: invasion and co-extinction waves....
  • 16. Fan, M., Kuang, Y.: Dynamics of a nonautonomous predator–prey system with the Beddington– DeAngelis functional response. J. Math. Anal....
  • 17. Gaines, R.E., Mawhin, J.L.: Coincidence Degree and Nonlinear Differential Equations. Springer, Berlin (1977)
  • 18. Lu, S.: On the existence of positive periodic solutions to a Lotka–Volterra cooperative population model with multiple delays. Nonlinear...
  • 19. Lu, S.: On the existence of positive periodic solutions for neutral functional differential equation with multiple deviating arguments....