Automatic synthesis of chaotic attractors using surrogate functions

Abstract

To automatically synthesize multi-scroll chaotic attractors, fundamental trade-offs on the nonlinear function must be analyzed and exploited. This paper proposes to use a surrogate function to approximate the trade-off between the operating frequency and the behavior of the switching points of the nonlinear function, which is a saturated nonlinear function series approximated by a piece-wise linear description. The surrogate function along with nonlinear system parameters and real physical active device parameters are used to compute all the parameters of the proposed nonlinear function. Later on, by using the synthesized nonlinear function, we develop an automatic synthesis methodology for multi-scroll chaotic attractors. Furthermore, to scale the frequency behavior of the chaotic attractors, we use other surrogate function that establishes a relation between the operating frequency and the scaling factor. Our results indicate that our synthesis methodology efficiently generates multi-scroll chaotic attractors, since nonlinear system parameters, real physical active device parameters and surrogate functions are used to compute not only all the parameters modeling the behavior of the nonlinear function, but chaotic attractor parameters are also computed. Numerical simulations and Hspice results illustrate the benefits of the new synthesis methodology.