TY - JOUR AU - Lian, K. Y. AU - Chiang, T. S. AU - Liu, P. PY - 2000 DA - 2000// TI - Discrete-time chaotic systems: applications in secure communications JO - Int. J. Bifurc. Chaos VL - 10 ID - Lian2000 ER - TY - JOUR AU - Feki, M. AU - Robert, B. AU - Gelle, G. AU - Colas, M. PY - 2003 DA - 2003// TI - Secure digital communication using discrete-time chaos synchronization JO - Chaos Solitons Fractals VL - 18 UR - https://doi.org/10.1016/S0960-0779(03)00065-1 DO - 10.1016/S0960-0779(03)00065-1 ID - Feki2003 ER - TY - JOUR AU - Guo, L. J. AU - Geng, X. Y. PY - 2005 DA - 2005// TI - Chaos communication based on synchronization of discrete-time chaotic systems JO - Chin. Phys. VL - 14 UR - https://doi.org/10.1088/1009-1963/14/2/010 DO - 10.1088/1009-1963/14/2/010 ID - Guo2005 ER - TY - CHAP AU - Stork, M. PY - 2009 DA - 2009// TI - Digital chaotic systems examples and application for data transmission BT - Proc. Int. Conf. Electrical & Electronics Eng. (ELECO’2009) ID - Stork2009 ER - TY - JOUR AU - Kocarev, L. AU - Szczepanski, J. AU - Amigo, J. M. AU - Tomovski, I. PY - 2006 DA - 2006// TI - Discrete chaos–I: theory JO - IEEE Trans. Circuits Syst. I, Regul. Pap. VL - 53 UR - https://doi.org/10.1109/TCSI.2006.874181 DO - 10.1109/TCSI.2006.874181 ID - Kocarev2006 ER - TY - JOUR AU - Hénon, M. PY - 1976 DA - 1976// TI - A two-dimensional mapping with a strange attractor JO - Commun. Math. Phys. VL - 50 UR - https://doi.org/10.1007/BF01608556 DO - 10.1007/BF01608556 ID - Hénon1976 ER - TY - JOUR AU - Lozi, R. PY - 1978 DA - 1978// TI - Un atracteur étrange du type attracteur de hénon JO - J. Phys. VL - 39 ID - Lozi1978 ER - TY - JOUR AU - Hitzl, D. AU - Zele, F. PY - 1985 DA - 1985// TI - An exploration of the Hénon quadratic map JO - Phys. D, Nonlinear Phenom. VL - 14 UR - https://doi.org/10.1016/0167-2789(85)90092-2 DO - 10.1016/0167-2789(85)90092-2 ID - Hitzl1985 ER - TY - JOUR AU - Baier, G. AU - Sahle, S. PY - 1995 DA - 1995// TI - Design of hyperchaotic flows JO - Phys. Rev. E VL - 51 UR - https://doi.org/10.1103/PhysRevE.51.R2712 DO - 10.1103/PhysRevE.51.R2712 ID - Baier1995 ER - TY - JOUR AU - Stefanski, K. PY - 1998 DA - 1998// TI - Modelling chaos and hyperchaos with 3D maps JO - Chaos Solitons Fractals VL - 9 UR - https://doi.org/10.1016/S0960-0779(97)00051-9 DO - 10.1016/S0960-0779(97)00051-9 ID - Stefanski1998 ER - TY - JOUR AU - Itoh, M. AU - Yang, T. AU - Chua, L. PY - 2001 DA - 2001// TI - Conditions for impulsive synchronization of chaotic and hyperchaotic systems JO - Int. J. Bifurc. Chaos VL - 11 UR - https://doi.org/10.1142/S0218127401002262 DO - 10.1142/S0218127401002262 ID - Itoh2001 ER - TY - BOOK AU - Wang, X. Y. PY - 2003 DA - 2003// TI - Chaos in Complex Nonlinear Systems PB - Publishing House of Electronics Industry CY - Beijing ID - Wang2003 ER - TY - JOUR AU - Atici, F. M. AU - Eloe, P. W. PY - 2009 DA - 2009// TI - Discrete fractional calculus with the nabla operator JO - Electron. J. Qual. Theory Differ. Equ. Spec. Ed. I VL - 2009 ID - Atici2009 ER - TY - JOUR AU - Abdeljawad, T. PY - 2011 DA - 2011// TI - On Riemann and Caputo fractional differences JO - Comput. Math. Appl. VL - 62 UR - https://doi.org/10.1016/j.camwa.2011.03.036 DO - 10.1016/j.camwa.2011.03.036 ID - Abdeljawad2011 ER - TY - JOUR AU - Abdeljawad, T. AU - Baleanu, D. AU - Jarad, F. AU - Agarwal, R. P. PY - 2013 DA - 2013// TI - Fractional sums and differences with binomial coefficients JO - Discrete Dyn. Nat. Soc. VL - 2013 ID - Abdeljawad2013 ER - TY - BOOK AU - Goodrich, C. AU - Peterson, A. C. PY - 2015 DA - 2015// TI - Discrete Fractional Calculus PB - Springer CY - German UR - https://doi.org/10.1007/978-3-319-25562-0 DO - 10.1007/978-3-319-25562-0 ID - Goodrich2015 ER - TY - JOUR AU - Baleanu, D. AU - Wu, G. AU - Bai, Y. AU - Chen, F. PY - 2017 DA - 2017// TI - Stability analysis of Caputo-like discrete fractional systems JO - Commun. Nonlinear Sci. Numer. Simul. VL - 48 UR - https://doi.org/10.1016/j.cnsns.2017.01.002 DO - 10.1016/j.cnsns.2017.01.002 ID - Baleanu2017 ER - TY - JOUR AU - Wu, G. AU - Baleanu, D. PY - 2013 DA - 2013// TI - Discrete fractional logistic map and its chaos JO - Nonlinear Dyn. VL - 75 UR - https://doi.org/10.1007/s11071-013-1065-7 DO - 10.1007/s11071-013-1065-7 ID - Wu2013 ER - TY - JOUR AU - Hu, T. PY - 2014 DA - 2014// TI - Discrete chaos in fractional Hénon map JO - Appl. Math. VL - 5 UR - https://doi.org/10.4236/am.2014.515218 DO - 10.4236/am.2014.515218 ID - Hu2014 ER - TY - JOUR AU - Shukla, M. K. AU - Sharma, B. B. PY - 2017 DA - 2017// TI - Investigation of chaos in fractional order generalized hyperchaotic Hénon map JO - Int. J. Electron. Commer. VL - 78 UR - https://doi.org/10.1016/j.aeue.2017.05.009 DO - 10.1016/j.aeue.2017.05.009 ID - Shukla2017 ER - TY - JOUR AU - Wu, G. C. AU - Baleanu, D. PY - 2015 DA - 2015// TI - Discrete chaos in fractional delayed logistic maps JO - Nonlinear Dyn. VL - 80 UR - https://doi.org/10.1007/s11071-014-1250-3 DO - 10.1007/s11071-014-1250-3 ID - Wu2015 ER - TY - JOUR AU - Boccaletti, S. AU - Grebogi, C. AU - Lai, Y. C. AU - Mancini, H. AU - Maza, D. PY - 2000 DA - 2000// TI - The control of chaos: theory and applications JO - Phys. Rep. VL - 329 UR - https://doi.org/10.1016/S0370-1573(99)00096-4 DO - 10.1016/S0370-1573(99)00096-4 ID - Boccaletti2000 ER - TY - JOUR AU - Fradkov, A. L. AU - Evans, R. J. AU - Andrievsky, B. R. PY - 2006 DA - 2006// TI - Control of chaos: methods and applications in mechanics JO - Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci. VL - 364 UR - https://doi.org/10.1098/rsta.2006.1826 DO - 10.1098/rsta.2006.1826 ID - Fradkov2006 ER - TY - JOUR AU - Pecora, L. M. AU - Carrol, T. L. PY - 1990 DA - 1990// TI - Synchronization in chaotic systems JO - Phys. Rev. A VL - 64 ID - Pecora1990 ER - TY - JOUR AU - Ouannas, A. AU - Azar, A. T. AU - Abu-Saris, R. PY - 2017 DA - 2017// TI - A new type of hybrid synchronization between arbitrary hyperchaotic maps JO - Int. J. Mach. Learn. Cybern. VL - 8 UR - https://doi.org/10.1007/s13042-016-0566-3 DO - 10.1007/s13042-016-0566-3 ID - Ouannas2017 ER - TY - JOUR AU - Ouannas, A. AU - Grassi, G. PY - 2016 DA - 2016// TI - A new approach to study co-existence of some synchronization types between chaotic maps with different dimensions JO - Nonlinear Dyn. VL - 86 UR - https://doi.org/10.1007/s11071-016-2966-z DO - 10.1007/s11071-016-2966-z ID - Ouannas2016 ER - TY - JOUR AU - Ouannas, A. AU - Odibat, Z. PY - 2015 DA - 2015// TI - Generalized synchronization of different dimensional chaotic dynamical systems in discrete-time JO - Nonlinear Dyn. VL - 81 UR - https://doi.org/10.1007/s11071-015-2026-0 DO - 10.1007/s11071-015-2026-0 ID - Ouannas2015 ER - TY - JOUR AU - Ouannas, A. PY - 2015 DA - 2015// TI - A new generalized-type of synchronization for discrete chaotic dynamical system JO - J. Comput. Nonlinear Dyn. VL - 10 UR - https://doi.org/10.1115/1.4030295 DO - 10.1115/1.4030295 ID - Ouannas2015 ER - TY - JOUR AU - Grassi, G. AU - Ouannas, A. AU - Pham, V. T. PY - 2018 DA - 2018// TI - A general unified approach to chaos synchronization in continuous-time systems (with or without equilibrium points) as well as in discrete-time systems JO - Arch. Control Sci. VL - 28 ID - Grassi2018 ER - TY - JOUR AU - Wu, G. AU - Baleanu, D. PY - 2014 DA - 2014// TI - Chaos synchronization of the discrete fractional logistic map JO - Signal Process. VL - 102 UR - https://doi.org/10.1016/j.sigpro.2014.02.022 DO - 10.1016/j.sigpro.2014.02.022 ID - Wu2014 ER - TY - JOUR AU - Wu, G. AU - Baleanu, D. AU - Xie, H. AU - Chen, F. PY - 2016 DA - 2016// TI - Chaos synchronization of fractional chaotic maps based on the stability condition JO - Physica A VL - 460 UR - https://doi.org/10.1016/j.physa.2016.05.045 DO - 10.1016/j.physa.2016.05.045 ID - Wu2016 ER - TY - JOUR AU - Liu, Y. PY - 2016 DA - 2016// TI - Chaotic synchronization between linearly coupled discrete fractional Hénon maps JO - Indian J. Phys. VL - 90 UR - https://doi.org/10.1007/s12648-015-0742-4 DO - 10.1007/s12648-015-0742-4 ID - Liu2016 ER - TY - JOUR AU - Megherbi, O. AU - Hamiche, H. AU - Djennoune, S. AU - Bettayeb, M. PY - 2017 DA - 2017// TI - A new contribution for the impulsive synchronization of fractional–order discrete–time chaotic systems JO - Nonlinear Dyn. VL - 90 UR - https://doi.org/10.1007/s11071-017-3743-3 DO - 10.1007/s11071-017-3743-3 ID - Megherbi2017 ER - TY - JOUR AU - Huang, L. L. AU - Baleanu, D. AU - Wu, G. C. AU - Zeng, S. D. PY - 2016 DA - 2016// TI - A new application of the fractional logistic map JO - Rom. J. Phys. VL - 61 ID - Huang2016 ER - TY - JOUR AU - Cermak, J. AU - Gyori, I. AU - Nechvatal, L. PY - 2015 DA - 2015// TI - On explicit stability condition for a linear fractional difference system JO - Fract. Calc. Appl. Anal. VL - 18 ID - Cermak2015 ER - TY - JOUR AU - Wu, G. C. AU - Baleanu, D. PY - 2015 DA - 2015// TI - Jacobian matrix algorithm for Lyapunov exponents of the discrete fractional maps JO - Commun. Nonlinear Sci. Numer. Simul. VL - 22 UR - https://doi.org/10.1016/j.cnsns.2014.06.042 DO - 10.1016/j.cnsns.2014.06.042 ID - Wu2015 ER - TY - JOUR AU - Kassim, S. AU - Hamiche, H. AU - Djennoune, S. AU - Bettayeb, M. PY - 2017 DA - 2017// TI - A novel secure image transmission scheme based on synchronization of fractional-order discrete-time hyperchaotic systems JO - Nonlinear Dyn. VL - 88 UR - https://doi.org/10.1007/s11071-017-3390-8 DO - 10.1007/s11071-017-3390-8 ID - Kassim2017 ER -