Page 546 - Mathematical Techniques of Fractional Order Systems

Chaotic Properties of Various Types of Hidden Attractors Chapter | 17 525

Hussian, G., Alnaser, M., Momani, S., 2008. Non-standard discretization of fractional differential
equations, in: Proceeding of 8th Seminar of Differential Equations and Dynamical Systems
in, Isfahan, Iran.
Ismail, S.M., Said, L.A., Radwan, A.G., Madian, A.H., Abu-ElYazeed, M.F., Soliman, A.M.,
2015. Generalized fractional logistic map suitable for data encryption, in: Science and
Technology (TICST), 2015 International Conference on, IEEE. pp. 336 341.
Jafari, S., Sprott, J., 2013. Simple chaotic flows with a line equilibrium. Chaos Solitons Fractals
57, 79 84.
Jafari, S., Sprott, J.C., Golpayegani, S.M.R.H., 2013. Elementary quadratic chaotic flows with
no equilibria. Phys. Lett. A 377, 699 702.
Jafari, S., Sprott, J.C., Nazarimehr, F., 2015. Recent new examples of hidden attractors. Eur.
Phys. J.
Kocarev, L., Lian, S., 2011. Chaos-based Cryptography: Theory, Algorithms and Applications,
Vol. 354. Springer, New York.
Kuznetsov, N.V., Leonov, G.A., 2014. Hidden attractors in dynamical systems: systems with no
equilibria, multistability and coexisting attractors. IFAC World Congress 19, 5445 5454.
Lau, F., Tse, C.K., 2003. Chaos-based Digital Communication Systems. Springer, New York.
Leonov, G.A., Kuznetsov, N.V., 2013. Hidden attractors in dynamical systems. from hidden
oscillations in Hilbert Kolmogorov, Aizerman, and Kalman problems to hidden chaotic
attractor in Chua circuits. Int. J. Bifurcat. Chaos 23, 1330002.
Li, C., Sprott, J.C., 2014. Coexisting hidden attractors in a 4-D simplified lorenz system. Int. J.
Bifurcat. Chaos 24, 1450034.
Magin, R.L., 2006. Fractional Calculus in Bioengineering. Begell House Redding, Redding.
Mickens, R.E., 2000. Applications of Nonstandard Finite Difference Schemes. World Scientific,
Hackensack, NJ.
Mickens, R.E., 2005. Advances in the Applications of Nonstandard Finite Difference Schemes.
World Scientific, Hackensack, NJ.
Moaddy, K., Radwan, A.G., Salama, K.N., Momani, S., Hashim, I., 2012. The fractional-order
modeling and synchronization of electrically coupled neuron systems. Comput. Math.
Applicat. 64, 3329 3339.
Molaie, M., Jafari, S., Sprott, J.C., Golpayegani, S.M.R.H., 2013. Simple chaotic flows with one
stable equilibrium. Int. J. Bifurcation Chaos 23, 1350188.
Mueller, S.T., 2011. Numerical method and step size variation in the lorenz equations. http://ir.
library.oregonstate.edu/xmlui/bitstream/handle/1957/25245/S.T.Mueller_Thesis.pdf.
Petras, I., 2011. Fractional-order Nonlinear Systems: Modeling, Analysis and Simulation.
Springer Science & Business Media, New York.
Pham, V.T., Volos, C., Jafari, S., Wang, X., Vaidyanathan, S., 2014. Hidden hyperchaotic
attractor in a novel simple memristive neural network. Optoelectr. Adv. Mater. Rapid
Commun. 8, 1157 1163.
Pham, V.T., Vaidyanathan, S., Volos, C.K., Jafari, S., 2015. Hidden attractors in a chaotic sys-
tem with an exponential nonlinear term. Eur. Phys. J. Spec. Topics 224, 1507 1517.
Pham, V.T., Vaidyanathan, S., Volos, C., Tlelo-Cuautle, E., Tahir, F.R., 2017a. A memristive
system with hidden attractors and its engineering application. Advances in Memristors,
Memristive Devices and Systems. Springer, New York, pp. 81 99.
Pham, V.T., Volos, C., Kapitaniak, T., 2017b. Synchronization of systems with hidden attractors.
Systems with Hidden Attractors. Springer, New York, pp. 65 77.
Pham, V.T., Volos, C., Kapitaniak, T., 2017c. Systems with hidden attractors: from theory to
realization in circuits.