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Articles

On planar zero-diagonal and zero-trace iterated maps

Pages 1521-1539 | Received 22 Mar 2018, Accepted 21 Jul 2018, Published online: 13 Aug 2018

References

  • D.R. Anderson, N.G. Myran, and D.L. White, Basins of attraction in a Cournot duopoly model of Kopel, J. Differ. Equ. Appl. 11(10) (2005), pp. 879–887. doi: 10.1080/10236190512331333888
  • K. Baron, and W. Jarczyk, Recent results on functional equations in a single variable, perspectives and open problems, Aequationes Math. 61(1–2) (2001), pp. 1–48. doi: 10.1007/s000100050159
  • G.I. Bischi, C. Mammana, and L. Gardini, Multistability and cyclic attractors in duopoly games, Chaos Soliton. Fract. 11(4) (2000), pp. 543–564. doi: 10.1016/S0960-0779(98)00130-1
  • A. Cournot, Recherches sur les Principes Mathematiques de la Theorie des Richesses. Translated as Researches into the Mathematical Principles of the Theory of Wealth (1963): p. 1838.
  • R.-A. Dana, and L. Montrucchio, Dynamic complexity in duopoly games, J. Econ. Theory. 40(1) (1986), pp. 40–56. doi: 10.1016/0022-0531(86)90006-2
  • F.M. Dannan, S.N. Elaydi, and V. Ponomarenko, Stability of hyperbolic and nonhyperbolic fixed points of one-dimensional maps, J. Differ. Equ. Appl. 9(5) (2003), pp. 449–457. doi: 10.1080/1023619031000078315
  • S. Elaydi, Discrete Chaos: With Applications in Science and Engineering, 2nd ed., Chapman & Hall/CRC, London, 2008.
  • A.A. Elsadany, Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization, Appl. Math. Comput. 294 (2017), pp. 253–263.
  • A.A. Elsadany, and A.E. Matouk, Dynamic Cournot duopoly game with delay, J. Complex Syst. 2014 (2014).
  • S. Kapcak, Stability of a Certain 2-Dimensional Map with Cobweb Diagram, Computational Science and Its Applications – ICCSA'16: 16th International Conference, Beijing, China (2016), Proceedings, Part I, Springer International Publishing, pp. 45–53.
  • S. Kapcak, U. Ufuktepe, and S. Elaydi, Stability and invariant manifolds of a generalized Beddington host-parasitoid model, J. Biol. Dyn. 7 (2013), pp. 233–253. doi: 10.1080/17513758.2013.849764
  • M. Kopel, Simple and complex adjustment dynamics in Cournot Duopoly model, Chaos Soliton. Fract. 7(12) (1996), pp. 2031–2048. doi: 10.1016/S0960-0779(96)00070-7
  • M. Kuczma, B. Choczewski, and R. Ger, Iterative Functional Equations, Cambridge University Press, Cambridge, 1990. No. 32.
  • Y.A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer-Verlag, New York, 1995. ISBN 0-387-94418-4.
  • Y.A. Kuznetsov, H.G. Meijer, and L. van Veen, The fold-flip bifurcation, Int. J. Bifurcat. Chaos 14(07) (2004), pp. 2253–2282. doi: 10.1142/S0218127404010576
  • J.H. Ma, and H. Tu, Complexity of a duopoly game in the electricity market with delayed bounded rationality, Discrete. Dyn. Nat. Soc. (2012). Article ID 698270. doi: 10.1155/2012/698270.
  • E. Maskin, and J. Tirole, A theory of dynamic oligopoly, I: Overview and quantity competition with large fixed costs, Econometrica J. Econ. Soc. 1 (1988), pp. 549–569. doi: 10.2307/1911700
  • E. Maskin, and J. Tirole, A theory of dynamic oligopoly, II: Price competition, kinked demand curves, and Edgeworth cycles, Econometrica J. Econ. Soc. 1 (1988), pp. 571–599. doi: 10.2307/1911701
  • K. Murakami, Stability for non-hyperbolic fixed points of scalar difference equations, J. Math. Anal. Appl. 310(2) (2005), pp. 492–505. doi: 10.1016/j.jmaa.2005.02.020
  • G.A. Pfeiffer, The functional equation f[f(x)]=g(x), Ann. Math. 20(1) (1918), pp. 13–22. Second Series, www.jstor.org/stable/1967374. doi: 10.2307/1967374
  • T. Puu, Chaos in Duopoly pricing, Chaos Soliton. Fract. 1 (6) (1991), pp. 573–581. doi: 10.1016/0960-0779(91)90045-B
  • Z. Sheng, J. Du, Q. Mei, and T. Huang, New analyses of Duopoly game with output lower limiters, Abstr. Appl. Anal. (2013), doi: 10.1155/2013/406743.
  • F. Tramontana, L. Gardini, and T. Puu, Global bifurcations in a piecewise-smooth Cournot duopoly game, Chaos Soliton. Fract. 43(1–12) (2010), pp. 15–24. doi: 10.1016/j.chaos.2010.07.001

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