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Original Articles

Global behaviour of a predator–prey like model with piecewise constant arguments

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Pages 159-171 | Received 10 Nov 2014, Accepted 04 May 2015, Published online: 04 Jun 2015

References

  • S. Banerjee and R.R. Sarkar, Delay-induced model for tumor-immune interaction and control of malignant tumor growth, Biosystems 91 (2008), pp. 268–288. doi: 10.1016/j.biosystems.2007.10.002
  • F. Bozkurt, Modeling a tumor growth with piecewise constant arguments, Discret. Dyn. Nat. Soc. (2013), Article ID 841764.
  • K.L. Cooke and I. Györi, Numerical approximation of the solutions of delay differential equations on an infinite interval using piecewise constant arguments, Comput. Math. Appl. 28 (1994), pp. 81–92. doi: 10.1016/0898-1221(94)00095-6
  • K. Gopalsamy and P. Liu, Persistence and global stability in a population model, J. Math. Anal. Appl. 224 (1998), pp. 59–80. doi: 10.1006/jmaa.1998.5984
  • F. Gurcan and F. Bozkurt, Global stability in a population model with piecewise constant arguments, J. Math. Anal. Appl. 360 (2009), pp. 334–342. doi: 10.1016/j.jmaa.2009.06.058
  • S. Kartal, Mathematical modeling and analysis of tumor-immune system interaction by using Lotka-Volterra predator–prey like model with piecewise constant arguments, PEN 2 (2014), pp. 7–12.
  • X. Li, C. Mou, W. Niu, and D. Wang, Stability analysis for discrete biological models using algebraic methods, Math. Comput. Sci. 5 (2011), pp. 247–262. doi: 10.1007/s11786-011-0096-z
  • P. Liu and K. Gopalsamy, Global stability and chaos in a population model with piecewise constant arguments, Appl. Math.Comput. 101 (1999), pp. 63–88. doi: 10.1016/S0096-3003(98)00037-X
  • R.M. May, Biological populations obeying difference equations: Stable points, stable cycles and chaos, J. Theor. Biol. 51 (1975), pp. 511–524. doi: 10.1016/0022-5193(75)90078-8
  • R.M. May and G.F. Oster, Bifurcations and dynamic complexity in simple ecological models, Am. Nat. 110 (1976), pp. 573–599. doi: 10.1086/283092
  • Y. Muroya, Persistence, contractivity and global stability in logistic equations with piecewise constant delays, J. Math. Anal. Appl. 270 (2002), pp. 602–635. doi: 10.1016/S0022-247X(02)00095-1
  • Y. Muroya, New contractivity condition in a population model with piecewise constant arguments, J. Math. Anal. Appl. 346 (2008), pp. 65–81. doi: 10.1016/j.jmaa.2008.05.025
  • I. Ozturk and F. Bozkurt, Stability analysis of a population model with piecewise constant arguments, Nonlinear Anal. Real. 12 (2011), pp. 1532–1545. doi: 10.1016/j.nonrwa.2010.10.011
  • I. Ozturk, F. Bozkurt, and F. Gurcan, Stability analysis of a mathematical model in a microcosm with piecewise constant arguments, Math. Biosci. 240 (2012), pp. 85–91. doi: 10.1016/j.mbs.2012.08.003
  • J.W.-H . So and J.S. Yu, Global stability in a logistic equation with piecewise constant arguments, Hokkaido Math. J. 24 (1995), pp. 269–286. doi: 10.14492/hokmj/1380892595
  • K. Uesugi, Y. Muroya, and E. Ishiwata, On the global attractivity for a logistic equation with piecewise constant arguments, J. Math. Anal. Appl. 294 (2004), pp. 560–580. doi: 10.1016/j.jmaa.2004.02.031