Models of nonlinear higher-order elements for autonomous fractional circuits

Abstract This article presents the synthesis of autonomous circuits that generate chaotic behavior using nonlinear fractional-order elements. It provides a comprehensive revision of the existing classification of nonlinear elements, including memory elements such as memristive and related systems, and extends this classification into the fractional-order domain. A similar generalization is applied to duality transformations. These transformations are then employed to derive a family of circuits exhibiting dual behavior, offering various implementation possibilities. The proposed methodology is demonstrated through a chaos generator whose nonlinear core is based on a memory version of a fractional resonance tank circuit.