References
- K.T. Alligood, T.D. Sauer and J.A. Yorke. CHAOS. An Introduction to Dynamical Systems. Springer-Verlag New York, Inc., 1997.
- G. Alvarez and S. Li. Breaking an encryption scheme based on chaotic baker map. Phys. Lett. A, 352:78–82, 2006. http://dx.doi.org/10.1016/j.physleta.2005.11.055.
- A. Anisimova, M. Avotina and I. Bula. Periodic orbits of single neuron models with internal decay rate 0 < β ≤ 1. Math. Model. Anal., 18:325–345, 2013. http://dx.doi.org/10.3846/13926292.2013.804462.
- F.A. Azevedo, L.R. Carvalho, L.T. Grinberg, J.M. Farfel, R.E. Ferretti, R.E. Leite, W.J. Filho, R. Lent and S. Herculano-Houzel. Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled-up primate brain. J. Comparative Neurology, 513:532–541, 2009. http://dx.doi.org/10.1002/cne.21974.
- Y. Chen. All solutions of a class of difference equations are truncated periodic. Appl. Math. Lett., 15:975–979, 2002. http://dx.doi.org/10.1016/S0893-9659(02)00072-1.
- R. Cheng. Oscillatory periodic solutions for two differential-difference equations arising in applications. Abstr. Appl. Anal., 2011: Article ID 635926, 12 pages, 2011. http://dx.doi.org/10.1155/2011/635926.
- S.N. Chow and H.O. Walther. Characteristic multipliers and stability of symmetric periodic solutions of ẋ(t) = g(x(t - 1)). Trans. Amer. Math. Soc., 307:127–142, 1988. http://dx.doi.org/10.1090/S0002-9947-1988-0936808-2.
- R. Devaney. An Introduction to Chaotic Dynamical Systems. second ed., Addison–Wesley, 1989.
- S.N. Elaydi. An Introduction to Difference Equations. second ed., Springer-Verlag New York, Inc., 1999.
- S.N. Elaydi. Discrete Chaos. With Applications in Science and Engineering. second ed., Chapman & Hall, CRC, 2008.
- K. Feltekh, Z.B. Jemaa, D. Fournier-Prunaret and S. Belghith. Border collision bifurcations and power spectral density of chaotic signals generated by one-dimensional discontinuous piecewise linear maps. Commun. Nonlinear Sci. Numer. Simul., 19:2771–2784, 2014. http://dx.doi.org/10.1016/j.cnsns.2013.12.029.
- M.R.S. Kulenovic and O. Merino. Discrete Dynamical Systems and Difference Equations with Mathematica. Chapman & Hall, CRC, 2002.
- R.D. Nussbaum. Uniqueness and nonuniqueness for periodic solutions of x' (t) = −g(x(t − 1)). J. Differential Equations, 34:25–54, 1979. http://dx.doi.org/10.1016/0022-0396(79)90016-0.
- H.O. Peitgen, H. Juergen and D. Saupe. Chaos and Fractals. New Frontiers of Science. second ed., Springer-Verlag New York, Inc., 2004.
- C. Robinson. Dynamical Systems. Stability, Symbolic Dynamics, and Chaos. CRC Press, Inc., 1995.
- R.C. Robinson. An Introduction to Dynamical Systems. Continuous and Discrete. Pearson Education, 2004.
- H.O. Walther. Homoclinic solutions and chaos in ẋ(t) = g(x(t - 1)). Nonlinear Anal., 5:775–788, 1981. http://dx.doi.org/10.1016/0362-546X(81)90052-3.
- Z. Wei, L. Huang and Y. Meng. Unboundedness and periodicity of solutions for a discrete-time network model of three neurons. Appl. Math. Model., 32:1463–1474, 2008. http://dx.doi.org/10.1016/j.apm.2007.06.016.
- J. Wu. Introduction to Neural Dynamics and Signal Transmission Delay. De Gruyter, Berlin, 2001.
- Z. Yuan, L. Huang and Y. Chen. Convergence and periodicity of solutions for a discrete-time network model of two neurons. Math. Comput. Model., 45:941–950, 2002. http://dx.doi.org/10.1016/S0895-7177(02)00061-4.
- Y. Zhou, L. Bao and C.L.P. Chen. A new 1d chaotic system for image encryption. Signal Processing, 97:172–182, 2014. http://dx.doi.org/10.1016/j.sigpro.2013.10.034.
- Z. Zhou. Periodic orbits on discrete dynamical systems. Comput. Math. Appl., 45:1155–1161, 2003. http://dx.doi.org/10.1016/S0898-1221(03)00075-0.
- Z. Zhou and J. Wu. Stable periodic orbits in nonlinear discrete-time neural networks with delayed feedback. Comput. Math. Appl., 45:935–942, 2003. http://dx.doi.org/10.1016/S0898-1221(03)00066-X.
- H. Zhu and L. Huang. Dynamics of a class of nonlinear discrete-time neural networks. Comput. Math. Appl., 48:85–94, 2004. http://dx.doi.org/10.1016/j.camwa.2004.01.006.