Behavioral Modeling of SNFS for Synthesizing Multi-Scroll Chaotic Attractors

Abstract

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.

Behavioral modeling for synthesizing n-scroll attractors

“…These differences are more prominent when the operating frequency of the chaotic attractors are pushed to operate in higher frequencies and this is due to that any information related with the real physical active device performance parameters is included in the numerical simulations. In this context, the works recently reported in [9,10] address not only the nonlinear modeling of an operational amplifier (Op Amp), including the most influential performance parameters, like the dynamic range (DR), gain bandwidth product (GB), DC gain (A DC ) and slew rate (SR), but based on that nonlinear model, the behavioral model of the saturated nonlinear function series (SNFS) along with the chaotic system were also derived and validated through numerical and experimental tests. This paper continues along the same line to study and enhance the generation of continuous time n-scroll attractors, but unlike [9,10], the current feedback operational amplifier (CFOA) is chosen as active device [11].…”

“…In this context, the works recently reported in [9,10] address not only the nonlinear modeling of an operational amplifier (Op Amp), including the most influential performance parameters, like the dynamic range (DR), gain bandwidth product (GB), DC gain (A DC ) and slew rate (SR), but based on that nonlinear model, the behavioral model of the saturated nonlinear function series (SNFS) along with the chaotic system were also derived and validated through numerical and experimental tests. This paper continues along the same line to study and enhance the generation of continuous time n-scroll attractors, but unlike [9,10], the current feedback operational amplifier (CFOA) is chosen as active device [11]. Because a CFOA presents better performance parameters than Op Amps, chaotic waveforms at 1-D can numerically be forecasted in higher frequencies [9,10] and with a better accuracy than those reported in [6,8].…”

“…1(a). In this way, following the analysis in [9,10], the behavioral model for SNFS can easily be deduced whether each basic block is modeled as shown in Fig. 1(b).…”

“…Once that the behavioral model for the n-building block has been deduced, the behavioral model for the SNFS can be derived [6,9,10] by modeling each basic block by (1) and (2). This means that the SNFS dynamic behavior is approached by a set of n-differential equations, which results in n þ 1 number of plateaus [9,10]. Therefore, each output voltage from Fig.…”

“…This paper continues along the same line to study and enhance the generation of continuous time n-scroll attractors, but unlike [9,10], the current feedback operational amplifier (CFOA) is chosen as active device [11]. Because a CFOA presents better performance parameters than Op Amps, chaotic waveforms at 1-D can numerically be forecasted in higher frequencies [9,10] and with a better accuracy than those reported in [6,8]. Experimental results are gathered, showing good agreement with numerical tests.…”