Robert Tchitnga

Dynamics of coupled simplest chaotic two-component electronic circuits and its potential application to random bit generation.

We numerically investigate the possibility of using a coupling to increase the complexity in simplest chaotic two-component electronic circuits operating at high frequency. We subsequently show that complex behaviors generated in such coupled systems, together with the post-processing are suitable for generating bit-streams which pass all the NIST tests for randomness. The electronic circuit is built up by unidirectionally coupling three two-component (one active and one passive) oscillators in a ring configuration through resistances. It turns out that, with such a coupling, high chaotic signals can be obtained. By extracting points at fixed interval of 10 ns (corresponding to a bit rate of 100 Mb/s) on such chaotic signals, each point being simultaneously converted in 16-bits (or 8-bits), we find that the binary sequence constructed by including the 10(or 2) least significant bits pass statistical tests of randomness, meaning that bit-streams with random properties can be achieved with an overall bit rate up to 10×100 Mb/s = 1 Gbit/s (or 2×100 Mb/s =200 Megabit/s). Moreover, by varying the bias voltages, we also investigate the parameter range for which more complex signals can be obtained. Besides being simple to implement, the two-component electronic circuit setup is very cheap as compared to optical and electro-optical systems.

Fractal-based analysis of optical coherence tomography data to quantify retinal tissue damage

BackgroundThe sensitivity of Optical Coherence Tomography (OCT) images to identify retinal tissue morphology characterized by early neural loss from normal healthy eyes is tested by calculating structural information and fractal dimension. OCT data from 74 healthy eyes and 43 eyes with type 1 diabetes mellitus with mild diabetic retinopathy (MDR) on biomicroscopy was analyzed using a custom-built algorithm (OCTRIMA) to measure locally the intraretinal layer thickness. A power spectrum method was used to calculate the fractal dimension in intraretinal regions of interest identified in the images. ANOVA followed by Newman-Keuls post-hoc analyses were used to test for differences between pathological and normal groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of each parameter to discriminate between eyes of pathological patients and normal healthy eyes.ResultsFractal dimension was higher for all the layers (except the GCL + IPL and INL) in MDR eyes compared to normal healthy eyes. When comparing MDR with normal healthy eyes, the highest AUROC values estimated for the fractal dimension were observed for GCL + IPL and INL. The maximum discrimination value for fractal dimension of 0.96 (standard error =0.025) for the GCL + IPL complex was obtained at a FD ≤ 1.66 (cut off point, asymptotic 95% Confidence Interval: lower-upper bound = 0.905-1.002). Moreover, the highest AUROC values estimated for the thickness measurements were observed for the OPL, GCL + IPL and OS. Particularly, when comparing MDR eyes with control healthy eyes, we found that the fractal dimension of the GCL + IPL complex was significantly better at diagnosing early DR, compared to the standard thickness measurement.ConclusionsOur results suggest that the GCL + IPL complex, OPL and OS are more susceptible to initial damage when comparing MDR with control healthy eyes. Fractal analysis provided a better sensitivity, offering a potential diagnostic predictor for detecting early neurodegeneration in the retina.

Chaos in a Single Op-Amp–Based Jerk Circuit: Experiments and Simulations

We report a five-component autonomous chaotic oscillator of jerky type, hitherto the simplest of its kind, using only one operational amplifier. The key component of the circuit is a junction field-effect transistor operating in its triode region, which provides a nonlinear resistor of antisymmetrical current-voltage characteristic, emulating a Colpitts-like chaotic circuit. We describe the experimental results illustrating the dynamical behavior of the circuit. In addition, we report numerical simulations of a model of the circuit which display good agreement with our measurements.

A novel high-frequency interpretation of a general purpose Op-Amp-based negative resistance for chaotic vibrations in a simple a priori nonchaotic circuit

A novel model of general purpose operational amplifiers is made to approximate, at best, the equivalent circuit for real model at high-frequency. With this new model, it appears that certain oscillators, usually studied under ideal considerations or using many existing real models of operational amplifiers, have hidden subtle and attractive chaotic dynamics that have previously been unknown. These can now be revealed. With the new considerations, a “two-component” circuit, consisting simply of a capacitor in parallel with a nonmodified (and usually presented as a linear, negative) resistance, tends to exhibit chaotic signals. P-Spice and laboratory experimental results are in good agreement with the theoretical predictions.

Stability of bright solitons in some physical systems

Dynamical systems described by the modified quintic complex Ginzburg Landau equation and its derivative forms are considered and the stability of their bright soliton solution is investigated numerically by means of the split-step Fourier method. Some discussions related to the way of ensuring the stability of this solution are presented.

FPGA Implementation of Linear Congruential Generator Based on Block Reduction Technique

This paper exposes circuit design of linear congruential generator (LCG) and implementation in FPGA based on block reduction technique. The circuit is derived from LCG algorithm proposed by Lehmer. Block reduction technique has been used to simplify the circuit. Several net connections among the blocks of the circuit are ignored or disconnected and the multiplier is replaced by a shifter. Simulations of both behavior and timing have been done and the results confirm its algorithm. The Cyclone II EP2C8Q208C8N and Cyclone IV E EP4CE115F29C7N of Altera have been chosen to extract comparison data of speed and occupied area. Further comparison of shift technique and the wordlengths reduction technique has been made. In general, the proposed design is far simpler than the previous published LCG circuit.

Coherent motion of chaotic attractors

We report a simple model of two drive-response-type coupled chaotic oscillators, where the response system copies the nonlinearity of the driver system. It leads to a coherent motion of the trajectories of the coupled systems that establishes a constant separating distance in time between the driver and the response attractors, and their distance depends upon the initial state. The coupled system responds to external obstacles, modeled by short-duration pulses acting either on the driver or the response system, by a coherent shifting of the distance, and it is able to readjust their distance as and when necessary via mutual exchange of feedback information. We confirm these behaviors with examples of a jerk system, the paradigmatic Rössler system, a tunnel diode system and a Josephson junction-based jerk system, analytically, to an extent, and mostly numerically.