A physical interpretation of fractional-order-derivatives in a jerk system: Electronic approach

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. (C) 2020 Elsevier B.V. All rights reserved.