A Novel Analog Electronic Circuit for Versatile Fractional Exponentiation.

The presence of nonlinear feedback is an effective method for generating chaos in dynamical systems. Although physics provides a plethora of nonlinear relationships that can be exploited for this purpose, engineering chaotic electronic circuits with prescribed nonlinear terms remain a formidable challenge. In particular, the implementation of fractional exponentiation represents a particularly challenging task. In this paper, we present a solution to this problem in the form of a new circuit topology, which we have designated as the "444 circuit", comprising only four transistors, four operational amplifiers, and four resistor pairs. In addition to multiplication and division, this circuit can perform complex algebraic operations, including the calculation of fractional powers. After introducing its operating principles and some conceptual aspects of its implementation, we demonstrate the performance of this unifying circuit structure by realizing a family of Lorenz-like systems. [ABSTRACT FROM AUTHOR]