Extension of unstable dissipative systems to the fractional-order case with applications in the design of multi-scroll attractors

Abstract Piecewise-linear unstable dissipative systems (UDS's) are a class of dynamical systems that are able to generate multi-scroll attractors through the spectral properties of their equilibria. The goal of this work is to extend the UDS's to the fractional-order case. To achieve it, a distance to the boundary of the fractional stability region is proosed in terms of the signed distance definition. The resulting definition covers both types of unstable dissipative systems and recovers the classical one in the integer-order case. For a given system, it also gives the range of fractional orders in which the system belongs to each type. The definition is applied to the design of two piecewise-linear systems that generate single-scroll and multi-scroll attractors. MSC Classification: 34A08 , 26A33 , 34A36 , 34D20 , 34C28