Behavioral Modeling of SNFS for Synthesizing Multi-Scroll Chaotic Attractors

Existing models of continuous nonlinear functions used for generating multi-scroll chaotic attractors are based on a piece-wise linear (PWL) approach. These models, although relatively easy to build, do not include any information related to the performance parameters of active devices, in the context of a possible physical implementation. This is a serious drawback, since the use of a PWL model introduces a level of inaccuracy into a numerical analysis which is more evident when numerical and experimental results are compared. This paper proposes a methodology to generate the behavioral model of continuous nonlinear functions, but unlike PWL approaches, real physical active device parameters are herein taken into account. In particular, we generate the behavioral model of a nonlinear function called saturated nonlinear function series (SNFS), but in general, the proposed approach can be used to generate the behavioral model of other continuous nonlinear functions. Our results indicate that the proposed approach yields a more realistic and accurate behavioral model than PWL models. As a consequence, not only the generation of chaotic attractors is more precise, but the metrics used to measure the complexity of a chaotic system can also be better predicted. Numerical and electrical simulation results at both domains, phase and time, illustrate the benefits of the new proposed model.