References
- X. Ai and Y. Sun, An optimal stopping problem in the stochastic Gilpin–Ayala population model, Adv. Differ. Equ. 2012 (2012). Article ID 210 (8 pages). doi: 10.1186/1687-1847-2012-210
- F.J. Ayala, M.E. Gilpin, and J.G. Eherenfeld, Competition between species: Theoretical models and experimental tests, Theor. Popul. Biol. 4 (1973), pp. 331–356. doi: 10.1016/0040-5809(73)90014-2
- F. Chen, Some new results on the permanence and extinction of nonautonomous Gilpin–Ayala type competition model with delays, Nonlinear Anal. 7(5) (2006), pp. 1205–1222. doi: 10.1016/j.nonrwa.2005.11.003
- F. Chen, X. Xie, and J. Shi, Existence, uniqueness and stability of positive periodic solution for a nonlinear prey-competition model with delays, J. Comput. Appl. Math. 194 (2006), pp. 368–387. doi: 10.1016/j.cam.2005.08.005
- H. Fang, Multiple positive periodic solutions for a food-limited two-species Gilpin–Ayala competition patch system with periodic harvesting terms, J. Inequal. Appl. 2012 (2012). Article ID 291 (17 pages). doi: 10.1186/1029-242X-2012-291
- H. Fang and Y. Wang, Four periodic solutions for a food-limited two-species Gilpin–Ayala type predator–prey system with harvesting terms on time scales, Adv. Differ. Equ. 2013 (2013), Article ID 278 (15 pages).
- M.E. Gilpin and F.J. Ayala, Global models of growth and competition, Proc. Natl. Acad. Sci. 70 (1973), pp. 3590–3593. doi: 10.1073/pnas.70.12.3590
- K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic Press, Dordrecht/Norwell, 1992.
- D. Guo, V. Lakshmikantham, and X. Liu, Nonlinear Integral Equations in Abstract Spaces, Mathematics and its Applications, Vol. 373, Kluwer Academic, Dordrecht, 1996.
- M. He, Z. Li, and F. Chen, Permanence, extinction and global attractivity of the periodic Gilpin–Ayala competition system with impulses, Nonlinear Anal. 11 (2010), pp. 1537–1551. doi: 10.1016/j.nonrwa.2009.03.007
- C. Huang and J. Cao, Impact of leakage delay on bifurcation in high-order fractional BAM neural networks, Neural Netw. 98 (2018), pp. 223–235. doi: 10.1016/j.neunet.2017.11.020
- C. Huang, J. Cao, and M. Xiao, Hybrid control on bifurcation for a delayed fractional gene regulatory network, Chaos Solitons Fractals 87 (2016), pp. 19–29. doi: 10.1016/j.chaos.2016.02.036
- C. Huang, J. Cao, M. Xiao, A. Alsaedi, and T. Hayat, Bifurcations in a delayed fractional complex-valued neural network, Appl. Math. Comput. 292 (2017), pp. 210–227.
- C. Huang, J. Cao, M. Xiao, A. Alsaedi, and F. Alsaadi, Controlling bifurcation in a delayed fractional predator–prey system with incommensurate orders, Appl. Math. Comput. 293 (2017), pp. 293–310.
- C. Huang, J. Cao, M. Xiao, A. Alsaedi, and F.E. Alsaadi, New bifurcation results for fractional BAM neural network with leakage delay, Chaos Solitons Fractals 100 (2017), pp. 31–44. doi: 10.1016/j.chaos.2017.04.037
- C. Huang, J. Cao, M. Xiao, A. Alsaedi, and T. Hayat, Effects of time delays on stability and Hopf bifurcation in a fractional ring-structured network with arbitrary neurons, Commun. Nonlinear Sci. Numer. Simul. 57 (2018), pp. 1–13. doi: 10.1016/j.cnsns.2017.09.005
- B. Lian and S. Hu, Asymptotic behaviour of the stochastic Gilpin–Ayala competition models, J. Math. Anal. Appl. 339 (2008), pp. 419–428. doi: 10.1016/j.jmaa.2007.06.058
- Q. Liu, Asymptotic properties of a stochastic n-species Gilpin–Ayala competitive model with Lévy jumps and Markovian switching, Commun. Nonlinear Sci. Numer. Simul. 26(1–3) (2015), pp. 1–10. doi: 10.1016/j.cnsns.2015.01.007
- H. Lu and G. Yu, Permanence of a Gilpin–Ayala predator–prey system with time-dependent delay, Adv. Differ. Equ. 2015 (2015). Article ID 109 (15 pages).
- A. Settati and A. Lahrouz, On stochastic Gilpin–Ayala population model with Markovian switching, Biosystems 130 (2015), pp. 17–27. doi: 10.1016/j.biosystems.2015.01.004
- D. Wang, Dynamic behaviors of an obligate Gilpin–Ayala system, Adv. Differ. Equ. 2016 (2016). Article ID 270 (10 pages).
- R. Wu, X. Zou, and K. Wang, Asymptotic properties of stochastic hybrid Gilpin–Ayala system with jumps, Appl. Math. Comput. 249 (2014), pp. 53–66.
- Y. Xing, M. Han, and G. Zheng, Initial value problem for first-order integro-differential equation of Volterra type on time scales, Nonlinear Anal. 60 (2005), pp. 429–442.
- K. Zhao and Y. Ren, Existence of positive periodic solutions for a class of Gilpin–Ayala ecological models with discrete and distributed time delays, Adv. Differ. Equ. 2017 (2017), Article ID 331 (13 pages).