Chameleon: the most hidden chaotic flow

Jafari, Mohammad; Mliki, Ezzedine; Akgül, Akif; Pham, Viet–Thanh; Kingni, Sifeu Takougang; Wang, Xiong; Jafari, Sajad

doi:10.1007/s11071-017-3378-4

Cited by 92 publications

(31 citation statements)

References 96 publications

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“…Although for numerical analysis of the proposed FOSRC system Adams-Bashforth-Moulton (ABM) [1,10,17] is used, for implementing the proposed FOSRC system in FPGA, the Adomian Decomposition Method (ADM) [5,14,36,56] is used. As because the ADM algorithm converges fast [5,14,25,56], the first 6 terms are used to get the solution of FONMCO system as in real cases. A time discretization method should be designed.…”

Section: Field Programmable Gate Array (Fpga) Implementation Of Fosrcmentioning

confidence: 99%

Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications

Rajagopal

Jafari

Kaçar

et al. 2019

ITC

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Chaos is often observed in forced nonlinear electrical circuits with saturable reactors. Simplest of such a circuit is presented and investigated in both integer order and non-integer (fractional) order form. For numerical analysis of fractional order system, the Adam-Bashforth-Moulton method is used. Some dynamic properties of the novel system are investigated. For implementing the system in field programmable gate arrays (FPGA), the Adomian decomposition method is used. Power and resource utilization of the fractional order system for implementing in FPGA are presented. Also, in this work, a novel fractional based sound encryption application is implemented as a unique application.

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Section: Field Programmable Gate Array (Fpga) Implementation Of Fosrcmentioning

confidence: 99%

Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications

Rajagopal

Jafari

Kaçar

et al. 2019

ITC

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“…The structural complexity of the self-excited and hidden attractors generated by the fractionalorder system (15) is analyzed by Equation (22). The SE is computed from the time series x(n) of the system (15) with length N = 4.5 × 10 4 .…”

Section: Structural Complexity Of the New Fractional-order Chaotic Symentioning

confidence: 99%

“…Hidden attractors are very important in engineering applications because they allow the study and understanding of the unexpected and potentially disastrous responses of the dynamical systems to perturbations, for instance, in mechanical structures, like a bridge or airplane wings [7][8][9], aircraft control systems [10], PLL circuits [1], drilling systems with induction motors [11], and secure communication schemes [1,12]. Hence, numerous integer-order chaotic flows with hidden attractors have been proposed [7,[13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors

Muñoz‐Pacheco

Zambrano-Serrano

Volos

et al. 2018

Entropy

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In this work, a new fractional-order chaotic system with a single parameter and four nonlinearities is introduced. One striking feature is that by varying the system parameter, the fractional-order system generates several complex dynamics: self-excited attractors, hidden attractors, and the coexistence of hidden attractors. In the family of self-excited chaotic attractors, the system has four spiral-saddle-type equilibrium points, or two nonhyperbolic equilibria. Besides, for a certain value of the parameter, a fractional-order no-equilibrium system is obtained. This no-equilibrium system presents a hidden chaotic attractor with a `hurricane’-like shape in the phase space. Multistability is also observed, since a hidden chaotic attractor coexists with a periodic one. The chaos generation in the new fractional-order system is demonstrated by the Lyapunov exponents method and equilibrium stability. Moreover, the complexity of the self-excited and hidden chaotic attractors is analyzed by computing their spectral entropy and Brownian-like motions. Finally, a pseudo-random number generator is designed using the hidden dynamics.

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“…When an attractors basin of attraction involves equilibrium, we call that attractor self-excited. Otherwise, the attractor is hidden [66][67][68][69][70][71]. Hidden attractors exist in some real-world dynamical systems [72][73][74].…”

Section: Equilibria Points and Finite-time Lyapunov Exponentsmentioning

confidence: 99%

Fractional Order Synchronous Reluctance Motor: Analysis, Chaos Control and FPGA Implementation

Rajagopal

Nazarimehr

Srinivasan³

et al. 2017

Asian Journal of Control

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This paper deals with the dynamical analysis and chaos control in a fractional order synchronous reluctance motor (FOSyncRM). Equilibrium points, characteristic equations and Eigen values of both commensurate and incommensurate FOSyncRM are presented. finite‐time Lyapunov exponents of the FOSyncRM system for fixed and varied parameters are investigated along with the bifurcation plots. Fractional order bifurcation plots are derived to show that the system shows more complex chaotic oscillations in fractional order. Chaos control in the FOSyncRM system is achieved using adaptive sliding mode controllers and the entire control algorithm is implemented in FPGA.

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Chameleon: the most hidden chaotic flow

Cited by 92 publications

References 96 publications

Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications

Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications

A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors

Fractional Order Synchronous Reluctance Motor: Analysis, Chaos Control and FPGA Implementation

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