Ecological Dynamics of a Predator-Prey Model with Cannibalism, Refuge, and Fear: A Bifurcation and Chaos Control Perspective

• Md. Jasim Uddin ^[1] ; Md. Mutakabbir Khan ^[1] ; Ibraheem M. Alsulami ^[2] ; Nehad Ali Shah ^[3]
  1. [1] University of Dhaka

     University of Dhaka

     DCC (Kotwali), Bangladés

     
  2. [2] Umm al-Qura University

     Umm al-Qura University

     Arabia Saudí

     
  3. [3] Sejong University

     Sejong University

     Corea del Sur

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 5, 2025
• Idioma: inglés
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• Resumen

  • Intraspecific predation, commonly known as cannibalism, is a naturally occurring phenomenon that significantly influences the structure and function of ecological systems. This study investigates the stability and bifurcation dynamics of a cannibalistic predator-prey model incorporating fear effects and prey refuge. We rigorously analyze the existence and stability conditions of the equilibrium points, demonstrating that the system exhibits complex behaviors, including period-doubling and NeimarkSacker bifurcations. The influence of key parameters—particularly the fear effect (φ) and step size (μ) –is examined as bifurcation parameters to assess their role in species coexistence and ecological balance. Numerical simulations validate theoretical results through phase portraits, bifurcation diagrams, Lyapunov exponent analysis, and local stability assessments. To mitigate chaotic dynamics, we implement Ott-Grebogi-Yorke (OGY) control, demonstrating its efficacy in stabilizing the system. By extending the analysis to a networked framework, we explore how coupling strength and network topology influence the dynamical behavior of interconnected predator–prey populations. Our findings provide critical insights into predator-prey interactions under behavioral adaptations, offering valuable implications for ecological conservation and sustainable species management. Varying fear intensity and refuge proportion results in noticeable transitions in population behavior, as evident in the bifurcation diagrams.

• Referencias bibliográficas
  • 1. Achar, S.J., Baishya, C., Veeresha, P., Akinyemi, L.: Dynamics of fractional model of biological pest control in tea plants with Beddington...
  • 2. Beddington, J.R.: Mutual interference between parasites or predators and its effect on searching efficiency. The Journal of Animal Ecology,...
  • 3. Crowley, P.H., Martin, E.K.: Functional responses and interference within and between year classes of a dragonfly population. J. N. Am....
  • 4. Deng, H., Chen, F., Zhu, Z., Li, Z.: Dynamic behaviors of Lotka Volterra predator prey model incorporating predator cannibalism. Adv. Difference...
  • 5. Diekmann, O., Nisbet, R.M., Gurney, W.S.C., Van den Bosch, F.: Simple mathematical models for cannibalism: a critique and a new approach....
  • 6. Gilarranz, L.J., Rayfield, B., Cembrano, L.G., Bascompte, J., Gonzalez, A.: Effects of network modularity on the spread of perturbation...
  • 7. Grilli, J., Rogers, T., Allesina, S.: Modularity and stability in ecological communities. Nat. Commun. 7(1), 12031 (2016)
  • 8. Guttal, V., Romanczuk, P., Simpson, S.J., Sword, G.A., Couzin, I.D.: Cannibalism can drive the evolution of behavioural phase polyphenism...
  • 9. Haque, M.: A detailed study of the Beddington DeAngelis predator prey model. Math. Biosci. 234(1), 1–16 (2011)
  • 10. Hassell, M.P., Varley, G.C.: New inductive population model for insect parasites and its bearing on biological control (1969)
  • 11. Holling, C.S.: Some characteristics of simple types of predation and parasitism1. Can. Entomol. 91(7), 385–398 (1959)
  • 12. Huang, Y., Chen, F., Zhong, L.: Stability analysis of a prey predator model with Holling type III response function incorporating a prey...
  • 13. Jacquet, C., Moritz, C., Morissette, L., Legagneux, P., Massol, F., Archambault, P., Gravel, D.: No complexity-stability relationship...
  • 14. Jin, W., Adamatzky, A.: Analysis of Parameter Space, Bifurcation and Symbolic Dynamics of Evolutionary Strategies on a One-Dimensional...
  • 15. Kang, Y., Rodriguez-Rodriguez, M., Evilsizor, S.: Ecological and evolutionary dynamics of two-stage models of social insects with egg...
  • 16. Kar, T.K.: Stability analysis of a prey predator model incorporating a prey refuge. Commun. Nonlinear Sci. Numer. Simul. 10(6), 681–691...
  • 17. Khan, A.Q.,Maqbool, A., Uddin,M.J., Rana, S.M.S.: Dynamical analysis of a two-dimensional discrete predator–prey model. Journal of Computational...
  • 18. Ko, W., Ryu, K.: Qualitative analysis of a predator prey model with Holling type II functional response incorporating a prey refuge. J....
  • 19. Lehtinen, S.O., Geritz, S.A.: Coevolution of cannibalistic predators and timid prey: evolutionary cycling and branching. J. Theor. Biol....
  • 20. Liu,M.,Wang, H., Jiang,W.: Bifurcations and pattern formation in a predator-prey model with memorybased diffusion. J. Differential Equations...
  • 21. Lotka, A.J.: Elements of physical biology. Williams & Wilkins (1925)
  • 22. Lynch, S.: others Dynamical systems with applications using Mathematica. Springer (2007)
  • 23. Ma, Z., Wang, S., Li, W., Li, Z.: The effect of prey refuge in a patchy predator prey system. Math. Biosci. 243(1), 126–130 (2013)
  • 24. Mezouaghi, A., Djilali, S., Bentout, S., Biroud, K.: Bifurcation analysis of a diffusive predator prey model with prey social behavior...
  • 25. Mukherjee, D.: The effect of prey refuges on a three species food chain model. Differential Equations Dynam. Systems 22(4), 413–426 (2014)
  • 26. Mutakabbir, K.M., Jasim U.M., Fahim, D., Islam, S., Sohel R.S.M., Qadeer K.A., Ali S.N.: Complex Dynamics of a Discrete Prey–predator...
  • 27. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Physical review letters, 64(11), (pp. 1196) (1990)
  • 28. Panja, P.: Dynamics of a predator prey model with crowley martin functional response, refuge on predator and harvesting of super-predator....
  • 29. Pizzatto, L., Shine, R.: The behavioral ecology of cannibalism in cane toads (Bufo marinus). Behav. Ecol. Sociobiol. 63, 123–133 (2008)
  • 30. Rayungsari, M., Suryanto, A., Kusumawinahyu, W.M., Darti, I.: Dynamical analysis of a predator-prey model incorporating predator cannibalism...
  • 31. Richardson, M.L., Mitchell, R.F., Reagel, P.F., Hanks, L.M.: Causes and consequences of cannibalism in noncarnivorous insects. Annu. Rev....
  • 32. Roy, S., Tiwari, P.K.: Multistability in a predator prey model with generalist predator and strong Allee effect in prey. The European...
  • 33. Roy, S., Tiwari, P.K.: Bistability in a predator prey model characterized by the Crowley Martin functional response: Effects of fear,...
  • 34. Roy, S., Tiwari, P.K., Nayak, H., Martcheva, M.: Effects of fear, refuge and hunting cooperation in a seasonally forced eco-epidemic model...
  • 35. Roy, S., Khajanchi, S., Tiwari, P.: Fear and its carry-over effects in a generalist predator prey system featuring cooperative hunting:...
  • 36. Sarkar, K., Khajanchi, S.: Impact of fear effect on the growth of prey in a predator-prey interaction model. Ecol. Complex. 42, 100826...
  • 37. Sarwardi, S., Mandal, P.K., Ray, S.: Analysis of a competitive prey predator system with a prey refuge. Biosystems 110(3), 133–148 (2012)
  • 38. Shabbir,M.S., Din, Q.: Understanding cannibalism dynamics in predator prey interactions: Bifurcations and chaos control strategies. Qualitative...
  • 39. Shabbir, M.S., Din, Q., Ahmad, K., Tassaddiq, A., Soori, A.H., Khan, M.A.: Stability, bifurcation, and chaos control of a novel discrete-time...
  • 40. Shabbir, M.S., Din, Q., Alabdan, R., Tassaddiq, A., Ahmad, K.: Dynamical complexity in a class of novel discrete-time predator-prey interaction...
  • 41. Singh, A., Malik, P.: Bifurcations in a modified Leslie Gower predator prey discrete model with Michaelis Menten prey harvesting. J. Appl....
  • 42. Uddin, M.J., Rana, S.M.S., I¸sık, S., Kangalgil, F.: On the qualitative study of a discrete fractional order prey–predator model with...
  • 43. Uddin, M.J., Rana, S.M.S.: Qualitative Analysis of the Discretization of a Continuous Fractional Order Prey-Predator Model with the Effects...
  • 44. Volterra, V.: Variazioni e fluttuazioni del numero d’individui in specie animali conviventi. Societ anonima tipografica" Leonardo...
  • 45. Wise, D.H.: Cannibalism, food limitation, intraspecific competition, and the regulation of spider populations. Annu. Rev. Entomol. 51(1),...
  • 46. Zhang, H., Cai, Y., Fu, S., Wang, W.: Impact of the fear effect in a prey-predator model incorporating a prey refuge. Appl. Math. Comput....
  • 47. Zhang, F., Chen, Y., Li, J.: Dynamical analysis of a stage-structured predator-prey model with cannibalism. Math. Biosci. 307, 33–41 (2019)