Chaotic properties of various types of hidden attractors in integer and fractional order domains


Nonlinear dynamical systems with chaotic attractors have many engineering applications such as dynamical models or pseudo-random number generators. Discovering systems with hidden attractors has recently received considerable attention because they can lead to unexpected responses to perturbations. In this chapter, several recent examples of hidden attractors, which are classified into several categories from two different viewpoints, are reviewed. From the viewpoint of the equilibrium type, they are classified into systems with no equilibria, with a line of equilibrium points, and with one stable equilibrium. The type of nonlinearity presents another method of categorization. System properties are explored versus the different parameters to identify the values corresponding to the presence of strange attractors. The behavior of the systems is explored for integer order and fractional order derivatives using the suitable numerical techniques. The studied properties include time series, phase portraits, and maximum Lyapunov exponent. © 2018 Elsevier Inc. All rights reserved.


Sayed W.S., Radwan A.G., Abd-El-Hafiz S.K.


Dynamical modeling; Encryption applications; Equilibrium points; Maximum lyapunov exponent; Mechanical systems; Phase portraits


Mathematical Techniques of Fractional Order Systems, PP. 503 to 528, Doi: 10.1016/B978-0-12-813592-1.00017-9

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Book Chapter

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