Fractional damping enhances chaos in the nonlinear Helmholtz oscillator

Ortiz, Adolfo; Yang, Jianhua; Coccolo, Mattia; Seoane, Jesús M.; Sanjuán, Miguel A. F.

doi:10.1007/s11071-020-06070-y

Cited by 10 publications

(1 citation statement)

References 19 publications

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“…Fractional-order derivatives are characterized by their memory properties providing an excellent approach for describing the physical phenomena elegantly with improved accuracy [1,2]. As a result, the researchers have proposed novel mathematical models with applications in various fields, such as biology, economics, chaos theory, botany, hidden dynamics, digital circuits, cryptography, control, image processing, wind turbines, viscoelastic studies, and ferroelectric materials [3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Active Realization of Fractional‐Order Integrators and Their Application in Multiscroll Chaotic Systems

et al. 2021

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This paper presents the design, simulation, and experimental verification of the fractional-order multiscroll Lü chaotic system. We base them on op-amp-based approximations of fractional-order integrators and saturated series of nonlinear functions. The integrators are first-order active realizations tuned to reduce the inaccuracy of the frequency response. By an exponential curve fitting, we got a convenient design equation for realizing fractional-order integrators of orders from 0.1 to 0.95. The results include simulations in SPICE of the mathematical description and the electronic implementation and experimental measurements that confirm them. Monte Carlo and sensitivity tests revealed a robust realization. Contrary to its passive counterparts, the suggested realizations significantly reduce design and implementation efforts by favoring resistors and capacitors with commercial values and reducing hardware requirements.

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