The Global Behavior of a Second Order Exponential Difference Equation
Download PDF
Authors: V. HADžIABDIć, J. BEKTEšEVIć AND M. MEHULJIć
DOI: 10.46793/KgJMat2505.781H
Abstract:
In this paper we present the Julia set and the global behavior of an exponential second order difference equation of the type
 |
where a ≥ 0, b > 0 and c > 0 with non-negative initial conditions.
Keywords:
Basin of attraction, period-two solutions, Julia set, difference equation.
References:
[1] A. M. Amleh, E. Camouzis and G. Ladas, On the dynamics of rational difference equation, Part I, Int. J. Differ. Equ. 3(1) (2008), 1–35.
[2] J. Bektešević, M. R. S. Kulenović and E. Pilav, Global dynamics of quadratic second order difference equation in the first quadrant, Appl. Math. Comput. 227 (2014), 50–65. https://doi.org/10.1016/j.amc.2013.10.048
[3] J. Bektešević, M. R. S. Kulenović and E. Pilav, Asymptotic approximations of the stable and unstable manifolds of fixed points of a two-dimensional quadratic map, J. Comput. Anal. Appl. 21(1) (2016), 35–51.
[4] J. Bektešević, M. R. S. Kulenović and E. Pilav, Asymptotic approximations of the stable and unstable manifolds of fixed points of a two-dimensional cubic map, Int. J. Differ. Equ. 10(1) (2015), 39–58.
[5] A. Brett and M. R. S. Kulenović, Basins of attraction of equilibrium points of monotone difference equations, Sarajevo J. Math. 5(18) (2009), 211–233.
[6] E. Camouzis and G. Ladas, Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures, Chapman and Hall/CRC, Boca Raton, London, 2008.
[7] Q. Din, E. M. Elabbasy, A. A. Elsadany and S. Ibrahim, Bifurcation analysis and chaos control of a second-order exponential difference equation, Filomat 33(15) (2019), 5003–5022. https://doi.org/10.2298/FIL1915003D
[8] S. Elaydi, An Introduction to Difference Equations, 3rd Edition, Springer - Verlag, New York, 2005.
[9] E. El-Metwally, E. A. Grove, G. Ladas, R. Levins and M. Radin, On the difference equation xn+1 = α + βxn−1e−xn, Nonlinear Anal. 47(7) (2001), 4623–4634. https://doi.org/10.1016/S0362-546X(01)00575-2
[10] H. Feng, H. Ma and W. Ding, Global asymptotic behavior of positive solutions for exponential form difference equation with three parameters, J. Appl. Anal. Comput. 6(3) (2016), 600–606. https://doi.org/10.11948/2016041
[11] E. A. Grove, G. Ladas, N. R. Prokup and R. Levis, On the global behavior of solutions of a biological model, Commun. Appl. Nonlinear Anal. 7(2) (2000), 33–46.
[12] M. R. S. Kulenović and G. Ladas, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman and Hall/CRC, Boca Raton, London, 2001.
[13] M. R. S. Kulenović and O. Merino, Invariant manifolds for competitive discrete systems in the plane, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 20(8) (2010), 2471–2486. https://doi.org/10.1142/S0218127410027118
[14] W. Wang and H. Feng, On the dynamics of positive solutions for the difference equation in a new population model, J. Nonlinear Sci. Appl. 9(4) (2016), 1748–1754. http://dx.doi.org/10.22436/jnsa.009.04.30
Login:
