345
Views
1
CrossRef citations to date
0
Altmetric
Special Issue in Memory of Abdul-Aziz Yakubu

Adaptive delayed reproduction in a 2-dimensional discrete-time competition model

Article: 2248171 | Received 16 Mar 2023, Accepted 10 Aug 2023, Published online: 17 Aug 2023

References

  • M. Bulmer, Theoretical Evolutionary Ecology, Sinauer Associates, Sunderland, Massachusetts, 1994.
  • O. de Feo and R. Ferriere, Bifurcation analysis of population invasion: On-off intermittency and basin riddling, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 10(2) (2000), pp. 443–452.
  • S. Elaydi and R.J. Sacker, Basin of attraction of periodic orbits of maps on the real line, J. Differ. Equ. Appl. 10(10) (2004), pp. 881–888.
  • S. Elaydi and A.-A. Yakubu, Global stability of cycles: Lotka-Volterra competition model with stocking, J. Differ. Equ. Appl. 8(6) (2002), pp. 537–549.
  • J.E. Franke and A.-A. Yakubu, Global attractors in competitive systems, Nonlinear Anal. 16(2) (1991), pp. 111–129.
  • J.E. Franke and A.-A. Yakubu, Mutual exclusion versus coexistence for discrete competitive systems, J. Math. Bio. 30(2) (1991), pp. 161–168.
  • M. Gatto, The evolutionary optimality of oscillatory and chaotic dynamics in simple population models, Theor. Popul. Biol. 43(3) (1993), pp. 310–336.
  • M. Hassell and H.N. Comins, Discrete time models for two-species competition, Theor. Popul. Biol. 9(2) (1976), pp. 202–221.
  • F. Hofbauer, J. Hofbauer, P. Raith, and T. Steinberger, Intermingled basins in a two species system, J. Math. Bio. 49(3) (2004), pp. 293–309.
  • J. Hofbauer, V. Hutson, and W. Jansen, Coexistence for systems governed by difference equations of lotka-volterra type, J. Math. Bio. 25(5) (1987), pp. 553–570.
  • H. Jiang and T.D. Rogers, The discrete dynamics of symmetric competition in the plane, J. Math. Bio. 25(6) (1987), pp. 573–596.
  • Y. Kang, Pre-images of invariant sets of a discrete-time two-species competition model, J. Differ. Equ. Appl. 18(10) (2011), pp. 1709–1733.
  • Y. Kang and H. Smith, Global dynamics of a discrete two-species Lottery-Ricker competition model, J. Biol. Dyn. 6(2) (2012), pp. 358–376.
  • R. Kon, Convex dominates concave: An exclusion principle in discrete-time Kolmogorov systems, Proc. Amer. Math. Soc. 134(10) (2006), pp. 3025–3034.
  • R. Luís, S. Elaydi, and H. Oliveira, Stability of a Ricker-type competition model and the competitive exclusion principle, J. Biol. Dyn. 5(6) (2011), pp. 636–660.
  • R.M. May and G.F. Oster, Bifurcations and dynamic complexity in simple ecological models, Am. Nat. 110(974) (1976), pp. 573–599.
  • S.D. Mylius and O. Diekmann, The resident strikes back: Invader-induced switching of resident attractor, J. Theoret. Biol. 211(4) (2001), pp. 297–311.
  • S. Tuljapurkar, Delayed reproduction and fitness in variable environments, Proc. Natl. Acad. Sci. USA 87(3) (1990), pp. 1139–1143.
  • A.-A. Yakubu, The effects of planting and harvesting on endangered species in discrete competitive systems, Math. Biosc. 126(1) (1995), pp. 1–20.
  • A.-A. Yakubu, A discrete competition system with planting, J. Differ. Equ. Appl. 4(2) (1998), pp. 213–214.