Automatic synthesis of chaotic attractors

An automatic synthesis methodology of multi-scroll chaotic attractors by using staircase nonlinear functions (SNFs) is introduced. Synthesis process is carried out by considering third-order nonlinear system parameters, such as the gain of the system and number of scrolls along with real physical active device parameters, such as the dynamic range. Therefore, it is not necessary done a scaling of the dynamic range associated to the SNFs and chaotic attractor parameters like the swings, widths, equilibrium points and breakpoints can be estimated. As a consequence, chaotic attractors in 1-direction (1-D) and 2-D n × m-grid scrolls can easily be generated. Moreover, from numerical simulations, the nonlinear system can quickly be synthesized with electronic circuits. HSPICE simulations of 9-scrolls and 4 × 3-grid scrolls by using Opamps are shown in agreement with the numerical simulations.