POINCARÉ PLANES IN NONLINEAR ELECTRONICS
Nonlinear element of a chaotic generator
A mathematical model of a nonlinear electronic circuit, which is the core of the electronic chaotic oscillator, is presented. This mathematical
model or nonlinear function has a direct relationship with the values of the components used to build an experimental electronic system.
In order to get a good approximation to the characteristic response curve of the nonlinear circuit, the mathematic model considers the
current-voltage curve of nonlinear elements.
Multivalued Synchronization by Poincaré Coupling
Multiscroll attractors by switching systems
In this paper, we present a class of three-dimensional dynamical systems having multiscrolls which we call unstable dissipative systems (UDSs). The UDSs are dissipative in one of its components but unstable in the other two. This class of systems is constructed with a switching law to display various multiscroll strange attractors. The multiscroll strange attractors result from the combination of several unstable “one-spiral” trajectories by means of switching. Each of these trajectories lies around a saddle hyperbolic stationary point. Thus, we describe how a piecewise-linear switching system yields multiscroll attractors, symmetric or asymmetric, with chaotic behavior.
Multimodal synchronization of chaos
An elementary notion of master–slave synchronization that accepts multimodal synchronization is introduced. We prove rigorously that the attractor of a coupled pair in a regime of multimodal synchronization is the graph of a multivalued function. Our framework provides the theoretical basis for some practical tools for detection of multimodal synchrony in experiments. Results are illustrated with the analysis of experiments with coupled electronic oscillators.
Forced synchronization of a self-sustained chaotic oscillator
This work presents a forced synchronization phenomenon like the asymptotic correlated behavior between chaotic oscillators forced by an external signal. Different kinds of forced synchronization are presented and given a theoretical justification explaining why it is possible to find some of them. Numerical results are presented for different cases such as antisymmetric, lag, phase, and identical forced synchronization.
Signal generator based on a chaotic circuit
Filtering by nonlinear systems
Synchronization of nonlinear systems forced by external signals is formalized as the response of a nonlinear filter. Sufficient conditions for a nonlinear system to behave as a filter are given. Some examples of generalized chaos synchronization are shown to actually be special cases of nonlinear filtering.
Set-Reset Flip-Flop Circuit with a Simple Output Logic
Electronic instrumentation of the Mexican Hat potential function
Electronic implementation of R2 lineal systems
A second order linear system suited for analog instrumentation is presented. Shown are the corresponding phase portrait nodes, a root focus
and a central point. The experimental prototype is of easy implementation and of low cost as it is comprised only of passive elements (i.e
resistors, capacitors) and operational ampliﬁers.
Discrete Coupling and Synchronization in the Insulin Release in the Mathematical Model of the Cells
Wavelet analysis of chaotic time series
In this work we analyzed experimental chaotic time series data from three known chaotic systems using the orthogonal wavelet transform. The experimental electronic implementation of the chaotic systems was used to analyze them. The wavelet analysis of the experimental chaotic time series, with a simple statistical approach, gives us useful information of such systems through the energy concentration at specific wavelet levels.
Pseudorandom Sequences in Spread-Spectrum Communications Generated by Cellular Automata
Dynamical systems methods have been recently used in spread-spectrum digital communication systems. The
expansion of the spectrum using a pseudorandom sequence with a higher frequency than the information signal is the
key feature for its robustness against the signal traveling interference through the channel. In this work, we propose to
generate pseudorandom sequences by employing cellular automata and we check these sequences have the
necessary properties which are required in modern communication systems. The computed sequences obtained by
the cellular automata are tested in a quadrature phase shift keying (QPSK) spread-spectrum communication system.
The efficiency of the system is analyzed by computing the bit error rate under different signal to noise ratio conditions.
These results are compared with systems that employ Golden code and other typical pseudorandom sequences.
Attractors generated from switching unstable dissipative systems
In this paper, we present a class of 3-D unstable dissipative systems, which are stable in two components but unstable in the other one. This class of systems is motivated by whirls, comprised of switching subsystems, which yield strange attractors from the combination of two unstable “one-spiral” trajectories by means of a switching rule. Each one of these trajectories moves around two hyperbolic saddle equilibrium points. Both theoretical and numerical results are provided for verification and demonstration.
A simple electronic circuit realization of the tent map
CHAOTIC DYNAMICS OF A NONLINEAR ELECTRONIC CONVERTER
A SIMPLE CIRCUIT WITH DYNAMIC LOGIC ARCHITECTURE OF BASIC LOGIC GATES
A MULTIVIBRATOR CIRCUIT BASED ON CHAOS GENERATION
A parameterized family of single-double-triple-scroll chaotic oscillations
We present a system with three equilibrium points which exhibit a single, double or triple scroll oscillation without introducing more equilibrium points. The study is based on one parameter of the nonlinear function which is the bifurcation parameter. With this bifurcation parameter it is possible to control the eigenvalues of the equilibrium points and consequently the type of oscillation.
A family of multimodal dynamic maps