R. Trejo-Guerra

CHAOTIC COMMUNICATION SYSTEM USING CHUA'S OSCILLATORS REALIZED WITH CCII+s

This work shows the experimental implementation of a chaotic communication system based on two Chuas oscillators which are synchronized by Hamiltonian forms and observer approach. The chaotic communication scheme is realized by using the commercially available positive-type second generation current conveyor (CCII+), which is included into the AD844 device. As a result, experimental measurements are provided to demonstrate the suitability of the CCII+ to implement chaotic communication systems.

Frequency limitations in generating multi-scroll chaotic attractors using CFOAs

The current-feedback operational amplifier (CFOA) allows us to implement any kind of circuit useful in analogue signal processing applications. However, it has limited performance in implementing nonlinear circuits. That way, this investigation highlights the experimental results of implementing a multi-scroll chaotic oscillator by using the commercially available CFOA AD844. The chaotic oscillator is based on saturated nonlinear function (SNLF) series, and we show and discuss its frequency limitations to generate 3- to 10-scrolls from 1 kHz to 100 kHz. Finally, we conclude that the frequency limitations are due to the nonideal characteristics of the CFOA-based SNLF block, imposed by the AD844.

A survey on the integrated design of chaotic oscillators

We present a review on the electronic design of chaotic oscillators. Multi-scroll chaotic oscillators are listed according to their electronic implementations. A 3-scrolls oscillator is analyzed from its mathematical description, and designed with current-feedback operational amplifiers. Finally, we list the integrated realizations, and discuss key points for future research on the design of multi-scroll chaotic oscillators.

Multiscroll floating gate–based integrated chaotic oscillator

In this work, we proposed a voltage-to-current cell based on a Complementary metal-oxide-semiconductor (CMOS) inverter designed by using floating gate transistors. We demonstrate its usefulness for the design of stair-type and sawtooth functions to be used in the implementation of a multiscroll chaotic oscillator. The main advantage of using floating gate transistors to design the nonlinear functions is the elimination of external reference DC sources, as is typically done in most of the nonlinear functions that generate multiscroll attractors. The key guidelines for the design of our proposed voltage-to-current cell are given to provide good performances in the design of an integrated multiscroll chaotic oscillator. HSPICE simulations are presented to demonstrate the usefulness of the proposed cell to generate multiscroll attractors. Finally, simulation results before and after layout are presented to show the good agreement with respect to theoretical results. HSPICE simulations of the post-layout design are in accordance with the system behavior. Copyright

On the trade-off between the number of scrolls and the operating frequency of the chaotic attractors

A trade-off analysis on the number of scrolls and the operating frequency is presented. To do so, nonlinear system parameters, real physical active device parameters and the operating frequency are taken into account to model the behavior of the saturated nonlinear function series approximated by a piecewise-linear description. As a consequence, not only the trade-off between the number of scrolls and the operating frequency is investigated, which depends directly on the behavior at the operating frequency of the nonlinear function, but also chaotic attractors are efficiently synthesized without the application of scaling techniques. Theoretical calculations are in good agreement with numerical simulations and a prediction on the maximum number of scrolls that can be synthesized for a particular frequency is also given.

Simulation of Chua’s chaotic oscillator using unity-gain cells

A novel topology to design a chaotic oscillator which is based on Chuas circuit, is proposed. The chaotic oscillator is realized with unity-gain cells, that is, the use of voltage followers (VF) and current followers (CF) to emulate the behavior of the two most important elements of the Chuas circuit: the active three-segment voltage controlled nonlinear resistor and the grounded inductor. Furthermore, it is shown that a negative current follower (CF-) can be implemented by using the IC AD844AN type current feedback operational amplifier (CFOA). The approach shows that the proposed topology can generate chaotic oscillations, where the HSPICE simulations have been obtained by using the macromodel of the IC AD844AN in configuration of unity-gain cell. Therefore, chaotic behavior in the time domain and the state space are presented.

Multiscroll oscillator based on floating gate CMOS inverter

The design of a multiscroll chaotic oscillator based on the realization of a sawtooth function by using floating gate MOSFETs (FGMOS), is introduced. Basically, we propose the implementation of a FGMOS inverter to generate the nonlinear functions which are responsible of the equilibrium points of a continuous chaotic dynamical system, allowing the generation of multiple scroll attractors. Spice simulations show the behavior of the nonlinear cell, along with the generation of multiscroll chaotic attractors.

Synchronization of n-scrolls chaotic systems synthesized from high-level behavioral modeling

The high-level modeling and simulation of a chaotic oscillator based on saturated functions (SFs) is presented for the synthesis of n-scrolls attractors from functional specifications. The applications of the synthesized chaotic circuits in a synchronization approach for secure communications are also described. The synthesis methodology is based on tree hierarchical levels. First, the oscillator is simulated at the electronic system level (ESL) by applying state variables and piecewise-linear approximation. Additionally, design space exploration of n-scroll attractors is performed by procedures to control the scaling of the excursion levels and frequency, R, L and C elements values and the breaking points and slopes of the SF. Second, SFs are synthesized using op-amp blocks. Verilog-A models are used to model the limitations (gain, bandwidth, slew-rate, saturation) of real op-amps. Theoretical results are confirmed by SPICE simulations to show the usefulness of the synthesis approach and the synchronization.

Synchronization of multi-directional multi-scroll chaos generators: A Hamiltonian approach

In this paper, a chaotic synchronization scheme for multi-directional multi-scroll chaos generators is presented. We use Generalized Hamiltonian forms approach to determine the synchronization conditions for two unidirectionally coupled multi-directional multi-scroll chaotic attractors. First, two state-variables of the master system are used to control the two nonlinear functions in the slave system and consequently, reach the synchronization of two 2D-4-scroll chaotic systems. Similarly, the synchronization of two 3D-4-scroll chaotic systems is achieved by using all three state-variables in order to control the three nonlinear functions for the slave system. Finally, theoretical calculations are in good agreement with numerical simulations and a prediction on the values for observer gain is also given.

Design and Applications of Continuous-Time Chaos Generators

Chaos systems can be classified as one type of complex dynamical systems that possess special features such as being extremely sensitive to tiny variations of initial conditions. In general, for deterministic chaos to exists, a dynamical systemmust have a dense set of periodic orbits, it must be transitive and it has to be sensitive to initial conditions (Strogatz, 2001). Chaos systems have bounded trajectories in the phase space, and they have at least one positive maximum Lyapunov exponent (Dieci, 2002; Lu et al., 2005; Munoz-Pacheco & Tlelo-Cuautle, 2010; Ramasubramanian & Sriram, 2000). Nowadays, several chaos generators have been implemented with electronic devices and circuits in order to have a major impact on many novel applications, as the ones reported in (Cruz-Hernandez et al., 2005; ErgunO Gamez-Guzman et al., 2008; Lin W Strogatz, 2001; Trejo-Guerra et al., 2009). Furthermore, this chapter is mainly devoted to highlight the design automation of continuous-time multi-scroll chaos generators, their implementations by using behavioral models of commercially available electronic devices, their experimental realizations and applications to secure communications. A review of the double-scroll Chua’s circuit is also presented along with the generation of hyperchaos by Coupling Two Chua’s circuits. Basically, we present the generation of multi-scroll attractors by using saturated nonlinear function series. We show their implementation by using traditional operational amplifiers (opamps) and current-feedback operational amplifiers (CFOAs) (Senani & Gupta, 1998). Besides, we summarize some performances of multi-scroll chaos generators by using opamps (Munoz-Pacheco & Tlelo-Cuautle, 2010), CFOAs (Trejo-Guerra, Sanchez-Lopez, Tlelo-Cuautle, Cruz-Hernandez & Munoz-Pacheco, 2010), current conveyors (CCs) (Sanchez-Lopez et al., 2010) and unity-gain cells (UGCs) (Sanchez-Lopez et al., 2008). However, not only the CC and the UGC can be taken from the commercially available CFOA AD844, but also they can be designed with standar integrated complementary metal-oxide-semiconductor (CMOS) technology (Trejo-Guerra, Tlelo-Cuautle, Munoz-Pacheco, Cruz-Hernandez & Sanchez-Lopez, 2010). 10