References

Journal of Mathematical Sciences: Advances and Applications

A SURVEY ON THE ENVELOPING METHOD OF SOME ONE-DIMENSIONAL NON-AUTONOMOUS DISCRETE PERIODIC POPULATION MODELS

[1] W. A. Coppel, The solution of equations by iteration, Mathematical Proceedings of the Cambridge Philosophical Society 51(01) (1955), 41-43.

[2] P. Cull, Stability in one-dimensional models, Scientiae Mathematicae Japonicae 58 (2003), 349-357.

[3] P. Cull, Enveloping implies global stability, In L. Allen, B. Aulbach, S. Elaydi and R. Sacker, editors, Difference Equations and Discrete Dynamical Systems, pages 170-181, Hackensack, NJ, 2005. World Scientific.

[4] P. Cull, Population models: Stability in one dimension, Bulletin of Mathematical Biology 69(3) (2007), 989-1017.

[5] P. Cull, K. Walsh and J. Wherry, Stability and instability in one-dimensional population models, Scientiae Mathematicae Japonicae Online pages 29-48, e-2008.

[6] J. Cushing and S. Henson, Global dynamics of some periodically forced, monotone difference equations, Journal of Difference Equations and Applications 7 (2001), 859-872.

[7] J. Cushing and S. Henson, A periodically forced Beverton-Holt equation, Journal of Difference Equation and Applications 8 (2002), 1119-1120.

[8] S. Elaydi, Discrete Chaos: With Applications in Science and Engineering, Chapman and Hall/CRC, Second Edition, 2008.

[9] S. Elaydi, R. Luis and H. Oliveira, Towards a theory of periodic difference equations and its application to population dynamics, In Mauricio Matos Peixoto, Alberto Adrego Pinto and David A. Rand, editors, Dynamics, Games and Science I, pages 287-321. DYNA 2008, in Honor of Maurcio Peixoto and David Rand, University of Minho, Braga, Springer, March 2011. Series: Springer Proceedings in Mathematics, Vol. 1.

[10] S. Elaydi and R. Sacker, Basin of attraction of periodic orbits of maps in the real line, Journal of Difference Equations and Applications 10 (2004), 881-888.

[11] S. Elaydi and R. Sacker, Global stability of periodic orbits of nonautonomous difference equations and populations biology, J. Differential Equations 208 (2005), 258-273.

[12] S. Elaydi and R. Sacker, Global stability of periodic orbits of nonautonomous difference equations in population biology and the Cushing-Henson conjectures, In Saber Elaydi, Gerasimos Ladas, Bernd Aulbach and Ondrej Dosly, editors, Proceedings of the Eighth International Conference on Difference Equations and Applications, pages 113-126, Chapman and Hall/CRC, 2005.

[13] S. Elaydi and R. Sacker, Nonautonomous Beverton-Holt equations and the Cushing-Henson conjectures, Journal of Difference Equations and Applications 11(4-5) (2005), 337-346.

[14] S. Elaydi and R. Sacker, Skew-product Dynamical Systems: Applications to Difference Equations, Proceedings of the Second Annual Celebration of Mathematics, United Arab Emirates, 2005.

[15] S. Elaydi and R. Sacker, Periodic difference equations, population biology and the Cushing-Henson conjectures, Mathematical Biosciences 201 (2006), 195-207.

[16] V. Kocic, A note on the nonautonomous Beverton-Holt model, Journal of Difference Equation and Applications 11(4-5) (2005), 415-422.

[17] R. Kon, A note on attenuant cycles of population models with periodic carrying capacity, Journal of Difference Equation and Applications 10(8) (2004), 791-793.

[18] E. Liz, Local stability implies global stability in some one-dimensional discrete single-species models, Discrete and Continuous Dynamical Systems-Series B 7(1) (2007), 191-199.

[19] A. Sharkovsky, Yu. Maistrenko and E. Romanenko, Difference Equations and their Applications, Kluwer Academic Publishers, London, 1993.

[20] J. Rubió-Massegú and Víctor Mañosa, On the enveloping method and the existence of global Lyapunov functions, Journal of Difference Equations and Applications 13(11) (2007), 1029-1035.

[21] R. Sacker, A note on periodic Ricker map, Journal of Difference Equations and Applications 13(1) (2007), 89-92.

[22] R. Sacker and J. Sell, Lifting properties in skew-product flows with applications to differential equations, AMS Memoirs 11(190), 1977.

[23] S. Stevic, A Short Proof of the Cushing-Henson conjecture, Discrete Dynamics in Nature and Society, Hindawi Publishing Corporation, 2006.

[24] J. Wright, Periodic systems of population models and enveloping functions, Computers and Mathematics with Applications 66 (2013), 2178-2195.