Ir al contenido

Documat


Bifurcation and Stability Analysis of a Discrete Predator–Prey Model with Alternative Prey

  • Ceyu Lei [1] ; Xiaoling Han [1] ; Weiming Wang [2]
    1. [1] Northwest Normal University

      Northwest Normal University

      China

    2. [2] Huaiyin Normal University

      Huaiyin Normal University

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
  • Idioma: inglés
  • DOI: 10.1007/s12346-024-01092-y
  • Enlaces
  • Resumen
    • In this paper, we investigate the dynamics of a class of discrete predator–prey model with alternative prey. We prove the boundedness of the solution, the existence and local/global stability of equilibrium points of the model, and verify the existence of flip bifurcation and Neimark-Sacker bifurcation. In addition, we use the maximum Lyapunov exponent and isoperimetric diagrams to verify the existence of periodic structures namely Arnold tongue and the shrimp-shaped structures in bi-parameter spaces of a class of predator–prey model.

  • Referencias bibliográficas
    • Plank, M.: Hamilton structure for -dimensional Lotka-Volterra equation. J. Math. Phys. 36, 3520–3534 (1995) Article MathSciNet Google Scholar...
    • Petrovskii, S., Morozov, A., Li, B.L.: Regimes of biological invasion in a predator-prey system with the Allee effect. Bull. Math. Biol. 67,...
    • Qiao, T., Cai, Y.L., et al.: Stability and Hopf bifurcation in a predator-prey model with the cost of anti-predator behaviors. Int. J. Bifur....
    • Ren, J.L., Li, X.P.: Bifurcations in a seasonally forced predator-prey model with generalized Holling type IV functional response. Int. J....
    • Verma, M., Misra, A.K.: Modeling the effect of prey refuge on a ratio-dependent predator-prey system with the Allee effect. Bull. Math. Biol....
    • Mishra, P., Wrzosek, D.: Pursuit-evasion dynamics for Bazykin-type predator-prey model with indirect predator taxis. J. Differ. Equ. 361,...
    • May, R.: Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976) Article Google Scholar
    • Lei, C.Y., Han, X.L., Wang, W.M.: Bifurcation analysis and chaos control of a discrete-time prey-predator model with fear factor. Math. Biosci....
    • Han, X.L., Lei, C.Y.: Bifurcation and Turing instability analysis for a space- and time-discrete predator-prey system with Smith growth function....
    • Streipert, S.H., Wolkowicz, G.S.K., Bohner, M.: Derivation and analysis of a discrete predator-prey model. Bull. Math. Biol. 84, 1–34 (2022) Article...
    • Din, Q.: Complexity and chaos control in a discrete-time prey-predator model. Commun. Nonlinear Sci. Numer. Simul. 49, 113–134 (2017) Article...
    • AlSharawi, Z., Pal, N., Chattopadhyay, J.: The role of vigilance on a discrete-time predator-prey model. Discrete Contin. Dyn. Syst. Ser....
    • Zhao, J.L.: Complexity and chaos control in a discrete-time Lotka-Volterra predator-prey system. J. Differ. Equ. Appl. 26, 1303–1320 (2020) Article...
    • Rajni, Ghosh B.: Multistability, chaos and mean population density in a discrete-time predator-prey system. Chaos Solitons Fractals 162, 112497...
    • Chen, Q.L., Teng, Z.D.: Codimension-two bifurcation analysis of a discrete predator-prey model with nonmonotonic functional response. J. Difference...
    • Rana, S., Bhowmick, A.R., Bhattacharya, S.: Impact of prey refuge on a discrete time predator-prey system with Allee effect. Int. J. Bifur....
    • Din, Q.: Complex dynamical behavior and control of a discrete ecological model. J. Vib. Control 29, 5270–5288 (2023) Article MathSciNet Google...
    • Muhammad, S.S., Din, Q., Manuel, D.L.S., et al.: Exploring dynamics of plant-herbivore interactions: bifurcation analysis and chaos control...
    • Muhammad, S.S., Din, Q.: Understanding cannibalism dynamics in predator-prey interactions: bifurcations and chaos control strategies. Qual....
    • Waqas, R., Din, Q., Khuram, K., et al.: Dynamics of predator-prey model based on fear effect with bifurcation analysis and chaos control....
    • Din, Q.: Dynamics and chaos control for a novel model incorporating plant quality index and larch budmoth interaction. Chaos Solitons Fractals...
    • Din, Q., Muhammad, I.K.: A discrete-time model for consumer-resource interaction with stability, bifurcation and chaos control. Qual. Theory...
    • Din, Q., Muhammad, A.Z.: Qualitative behavior of a discrete predator-prey system under fear effects. Z. Naturforsch. A 77, 1023–1043 (2022) Article...
    • Ricker, W.E.: Stock and recruitment. J. Fish. Board. Can. 11, 559–623 (1954) Article Google Scholar
    • McCallum, H.I.: Effects of immigration on chaotic population dynamics. J. Theor. Biol. 154, 277–284 (1992) Article Google Scholar
    • Sinha, S., Parthasarathy, S.: Unusual dynamics of extinction in a simple ecological model. Proc. Natl. Acad. Sci. 93, 1504–1508 (1996) Article...
    • Agiza, H.N., Elabbasy, E.M., et al.: Chaotic dynamics of a discrete prey-predator model with Holling-Type II. Nonlinear Anal. Real World Appl....
    • Cheng, L.F., Cao, H.J.: Bifurcation analysis of a discrete-time ratio-dependent predator-prey model with Allee effect. Commun. Nonlinear Sci....
    • Singh, A., Sharma, V.S.: Bifurcations and chaos control in a discrete-time prey-predator model with Holling type-II functional response and...
    • Cui, W.Z., Zhao, Y.L.: Bifurcation analysis of a predator-prey model with alternative prey and prey refuges. Internat. J. Bifur. Chaos Appl....
    • Arancibia, I.C., Flores, J., Bode, M., et al.: A modified May-Holling-Tanner predator-prey model with multiple Allee effects on the prey and...
    • Yuan, L.G., Yang, Q.G.: Bifurcation, invariant curve and hybrid control in a discrete-time predator-prey system. Appl. Math. Model 39, 2345–2362...
    • Chen, G.Y., Teng, Z.D., Hu, Z.Y.: Analysis of stability for a discrete ratio-dependent predator-prey system. Indian J. Pure Appl. Math. 42,...
    • Yang, X.T.: Uniform persistence and periodic solutions for a discrete predator-prey system with delays. J. Math. Anal. Appl. 316, 161–177...
    • Wang, L., Wang, M.: Ordinary Difference Equation. Xinjiang University Press, Xinjiang (1989) Google Scholar
    • Sevval, Y., Seyma, B., Hüseyin, M.: Stability and bifurcation analyses of a discrete Lotka-Volterra type predator-prey system with refuge...
    • Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. Springer-Verlag, New York (2004) Book Google Scholar
    • Nicholas, F.B.: Essential Mathematical Biology. Springer-Verlag, London (2003) Google Scholar
    • Gallas, J.A.C.: Structure of the parameter space of the Hénon map. Phys. Rev. Lett. 70, 2714–2717 (1993) Article Google Scholar
    • Layek, G.C., Pati, N.C.: Organized structures of two bidirectionally coupled logistic maps. Chaos 29, 093104 (2019)

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno