N-scroll chaotic attractors from saturated function series employing CCII+s

Abstract

The generation of n-scroll chaotic attractors by using saturated nonlinear function series (SNFS) realized with positive-type second generation current conveyors (CCII+s), is introduced. The nonlinear dynamical system is expressed by a third-order differential equation and to carry out numerical simulations, SNFS are ideally modeled by using staircase functions. Therefore, numerical simulations are introduced to approximate the swings, widths, breakpoints and equilibrium points of the n-scroll attractors by considering, as input variables: the dynamic range associated C. Sánchez-López ( ) to active devices, gain of the nonlinear system and the number of scrolls. Therefore, its dynamical behavior is investigated in the state space. Besides, the CCII± is a versatile analog building block and it has been demonstrated to be very useful in several linear and nonlinear applications, since CCII-based implementations offer better performances that Opamps-based implementations in terms of accuracy and bandwidth. Therefore, the nonlinear system is synthesized with CCII+s to generate 3-and 4-scrolls. HSPICE simulations and experimental results are shown to verify the agreement on the behavior of the proposed circuit and the numerical simulations.

Behavioral modeling for synthesizing n-scroll attractors

“…, Bp j is the j-th breakpoint [6,7] and each AEBp is a DC voltage source which is used to compare if xðtÞ is larger or smaller than AEBp. 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).…”

“…Particularly on the generation of continuous time n-scroll attractors by using universal active devices [2,3], a piece-wise linear (PWL) approach is often used to model the nonlinear part of the third order chaotic system [4,5,6,7,8]. Despite of that PWL models are relatively easy to build and numerical simulations can be realized, in practice, the predicted performance of the chaotic system differs substantially from reality.…”

“…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.…”

Design and Applications of Continuous-Time Chaos Generators

“…A significant feature of these functions is that they are smooth enough to possess convergent Taylor expansions at all points and consequently can be linearized (Strogatz, 2001). A type of nonlinear function frequently used in system modeling is the piecewise-linear (PWL) approximation, which consists of a set of linear relations valid in different regions (Elhadj & Sprott, 2010;Lin & Wang, 2010;Lü et al, 2004;Muñoz-Pacheco & Tlelo-Cuautle, 2009;Sánchez-López et al, 2010;Suykens et al, 1997;Yalçin et al, 2002). The use of PWL approximations have the advantage that the dynamical equations become linear or linearized in any particular region, and hence the solutions for different regions can be joined together at the boundaries.…”

Stability and Multiscroll Attractors of Control Systems via the Abscissa

“…One of the different chaotic behaviors is the presence of multiscroll attractor. Good references where the generation of multiscrolls has been studied are the works [28][29][30][31][32][33][34][35]. In this paper we use the abscissa of stability of Hurwitz polynomials to study the stability of systems in order to generate multiscroll attractors.…”