Commun Nonlinear Sci Numer Simulat 90 (2020) 105413 Contents lists available at ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns Research paper A physical interpretation of fractional-order-derivatives in a jerk system: Electronic approach J.L. Echenausía-Monroy a , H.E. Gilardi-Velázquez a,b , R. Jaimes-Reátegui a , V. Aboites c , G. Huerta-Cuellar a,d,∗ a Dynamical Systems Laboratory, CULagos, Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, Lagos de Moreno, 47460, Jalisco, México b Facultad de Ingeniería, Universidad Panamericana Josemaría Escrivá de Balaguer 101, Aguascalientes, Aguascalientes, 20290, México c Centro de Investigaciones en Óptica, CIO, Loma del Bosque 115, Col. Campestre, León, 37150, GTO, México d Applied Mathematics Division, Instituto Potosino de Investigación Científica y Tecnológica, IPICYT, Camino a la Presa San José 2055, Col. Lomas 4ta. Sección, 78216, San Luis Potosí, S. L. P., México a r t i c l e i n f o Article history: Received 13 March 2020 Revised 13 May 2020 Accepted 16 June 2020 Available online 17 June 2020 Keywords: Fractional order derivatives Electronic implementation Jerk systems Numerical analysis a b s t r a c t In this paper, a physical interpretation of the fractional-order-derivatives effects in a jerk system, based on Unstable Dissipative Systems (UDS), and a Saturated Non-Linear Func- tion (SNLF), is presented. The system is electronically implemented in Multisim develop- ment platform for a 9-scrolls attractor generation. The behavior is analyzed trough the Detrended Fluctuation Analysis (DFA), Probability Density Function (PDF), bifurcation dia- grams, and the implementation of a geometrical analysis of the phase space. The changes that the system undergoes when a fractional-order are analyzed. The results show that when the fractional integration-orders are considered, the areas of the generated attrac- tor are modified with respect to the integer-order dynamic. The long-range correlations in the system are also modified because of the fractional-orders. Besides, a particular phe- nomenon in the equilibrium points preference occurs, which is induced when the frac- tional integration-order is applied in only one of the state variables. © 2020 Elsevier B.V. All rights reserved. 1. Introduction With the implementation of fractional calculus theory, developed almost 300 years ago, the study of chaotic systems through fractional-order-derivatives, has been extensively studied by the scientific community [1–3], due to the memory and hereditary properties that presents several natural materials and processes [4,5]. In the same way as in integer-order systems, numerous publications describe the implementation of chaotic systems under fractional-order schemes, such as the Duffing oscillator [6], the Chua system [7], the Rössler system [8], the Chen generator [9], the Lü model [10], among many others, where it is verified that the implementation of non-integer orders in this kind of systems preserves the chaotic be- havior [11–13]. However, few comparative analyzes show, quantitatively, the changes that occur in the dynamics of a system when contemplating fractional orders, against the natural dynamics of the model when is analyzed with an integration-order equal to the unit [14]. ∗ Corresponding author at: Dynamical Systems Laboratory, CULagos, Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, 47460 Lagos de Moreno, Jalisco, México. E-mail address: g.huerta@lagos.udg.mx (G. Huerta-Cuellar). https://doi.org/10.1016/j.cnsns.2020.105413 1007-5704/© 2020 Elsevier B.V. All rights reserved.