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

Abstract 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 Function (SNLF), is presented. The system is electronically implemented in Multisim development platform for a 9-scrolls attractor generation. The behavior is analyzed trough the Detrended Fluctuation Analysis (DFA), Probability Density Function (PDF), bifurcation diagrams, 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 attractor 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 phenomenon in the equilibrium points preference occurs, which is induced when the fractional integration-order is applied in only one of the state variables.

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