Behavioral modeling for synthesizing n-scroll attractors

Abstract

In this letter, the nonlinear behavioral model of a thirdorder chaotic system based on CFOAs is introduced. The proposed model is more realistic than PWL approaches widely used in the literature, since herein real physical active device performance parameters along with its parasitic elements are taken into account in the modeling process. As a consequence, chaotic attractors at 1-D can not only be better forecasted, but since chaotic waveforms numerically and experimentally generated have a random behavior, statistical tests are used to measure the similitude between them. Experimental results of the chaotic system designed with the AD844AN integrated circuit are gathered, showing good agreement with theoretical simulations.

Adaptive Synchronization of Chaotic Systems considering Performance Parameters of Operational Amplifiers

“…Several nonlinear functions can be used for modeling ( , ( )) in (1) and (2), such as sgn( , ( )) functions, staircase functions, hysteresis functions, saw-tooth functions, and, herein, a saturated nonlinear function series (SNFS), which is traditionally modeled by using a PWL approach [15]. Moreover, the dimensionless dynamical systems (1) and (2) can be built with either Op Amp [17] or CFOA [22]. In this paper, the former case is considered and the equivalent circuit, taken from [17], is shown in Figure 1.…”

“…Additional information about Figure 1 and the deduction of (10) can be found in [17]. Notice that DC , GB, SR, and DR are the main performance parameters of an Op Amp [17,22]. It is worth mentioning that (10) involves the nonlinear model for SNFS including the most influential performance parameters associated with Op Amps, whereas the rest of amplifiers, those placed horizontally in Figure 1, are ideally considered.…”

“…Now that we have the behavioral models for the transmitter and receiver along with the synchronization scheme given by (10) and (16), respectively, we can use them to do numerical simulations by using the fourth-order Runge-Kutta algorithm with time step 2 −6 . It is worth mentioning that unlike the synchronization methods previously reported, PWL functions are used to design the nonlinear part of the chaotic oscillator and as a consequence a level of inaccuracy is introduced into a numerical analysis, which is more evident when numerical and experimental results are compared [17,21,22]. Meanwhile, the behavioral models previously deduced take into account the real physical active device parameters and hence, the synchronization of chaotic waveforms between the transmitter and receiver is better forecasted.…”

“…The reason of that is the fact that no information related with the real physical active device performance parameters is included in the numerical simulations [18][19][20]. Only in recent years, the works reported in [17,21,22] led the nonlinear behavior of a third-order dynamical system including the most influential performance parameters of Operational Amplifiers (Op Amp) and Current-Feedback Operational Amplifiers 2 Advances in Mathematical Physics (CFOA). The nonlinear behavior of both dynamical systems was validated through experimental tests, confirming a good agreement with numerical tests.…”

“…In this sense and for realization of communication systems based on chaos with high performance, it is of vital significance to take into account the real physical active device performance parameters, in order to develop communication systems with a practically usable performance [5]. Therefore, as natural evolution from [17,22], this paper leads to improving the synchronization of multiscroll chaotic attractors by considering those more important performance parameters associated with the active devices used for synthesizing the dynamical systems and the synchronization block, in order to achieve a robust and cheap communication system based on chaos. The outline of the paper is the following: an adaptive control law to synchronize chaotic waveforms of the receiver with that coming from the transmitter is introduced in Section 2, where the adaptive control is embedded in the receiver.…”