390 research outputs found
Bifurcations and synchronization using an integrated programmable chaotic circuit
This paper presents a CMOS chip which can act as an autonomous stand-alone unit to generate different real-time chaotic behaviors by changing a few external bias currents. In particular, by changing one of these bias currents, the chip provides different examples of a period-doubling route to chaos. We present experimental orbits and attractors, time waveforms and power spectra measured from the chip. By using two chip units, experiments on synchronization can be carried out as well in real-time. Measurements are presented for the following synchronization schemes: linear coupling, drive-response and inverse system. Experimental statistical characterizations associated to these schemes are also presented. We also outline the possible use of the chip for chaotic encryption of audio signals. Finally, for completeness, the paper includes also a brief description of the chip design procedure and its internal circuitry
Discrete-Time Chaotic-Map Truly Random Number Generators: Design, Implementation, and Variability Analysis of the Zigzag Map
In this paper, we introduce a novel discrete chaotic map named zigzag map
that demonstrates excellent chaotic behaviors and can be utilized in Truly
Random Number Generators (TRNGs). We comprehensively investigate the map and
explore its critical chaotic characteristics and parameters. We further present
two circuit implementations for the zigzag map based on the switched current
technique as well as the current-mode affine interpolation of the breakpoints.
In practice, implementation variations can deteriorate the quality of the
output sequence as a result of variation of the chaotic map parameters. In
order to quantify the impact of variations on the map performance, we model the
variations using a combination of theoretical analysis and Monte-Carlo
simulations on the circuits. We demonstrate that even in the presence of the
map variations, a TRNG based on the zigzag map passes all of the NIST 800-22
statistical randomness tests using simple post processing of the output data.Comment: To appear in Analog Integrated Circuits and Signal Processing (ALOG
Deterministic polarization chaos from a laser diode
Fifty years after the invention of the laser diode and fourty years after the
report of the butterfly effect - i.e. the unpredictability of deterministic
chaos, it is said that a laser diode behaves like a damped nonlinear
oscillator. Hence no chaos can be generated unless with additional forcing or
parameter modulation. Here we report the first counter-example of a
free-running laser diode generating chaos. The underlying physics is a
nonlinear coupling between two elliptically polarized modes in a
vertical-cavity surface-emitting laser. We identify chaos in experimental
time-series and show theoretically the bifurcations leading to single- and
double-scroll attractors with characteristics similar to Lorenz chaos. The
reported polarization chaos resembles at first sight a noise-driven mode
hopping but shows opposite statistical properties. Our findings open up new
research areas that combine the high speed performances of microcavity lasers
with controllable and integrated sources of optical chaos.Comment: 13 pages, 5 figure
Topics in chaotic secure communication
Results in nonlinear dynamics and chaos during this decade have been applied to problems in secure communications with limited success. Most of these applications have been based on the chaotic synchronization property discovered by Pecora and Carroll in 1989 [37]. Short [44, 45, 48] demonstrated the effectiveness of nonlinear dynamic (NLD) forecasting methods in breaking this class of communication schemes. In response, investigators have proposed enhancements to the basic synchronization technique in an attempt to improve the security properties. In this work two of these newer communication systems will be analyzed using NLD forecasting and other techniques to determine the level of security they provide. It will be shown that the transmitted waveform alone allows an eavesdropper to extract the message.
During the course of this research, a new impulsively initialized, binary chaotic communication scheme has been developed, which eliminates the most significant weaknesses of its predecessors. This new approach is based on symbolic dynamics and chaotic control, and may be implemented using one-dimensional maps, which gives the designer more control over the statistics of the transmitted binary stream. Recent results in a certain class of one-dimensional chaotic maps will be discussed in this context.
The potential for using NLD techniques in problems from standard digital communications will also be explored. The two problems which will be addressed are bit errors due to channel effects and co-channel interference. It will be shown that NLD reconstruction methods provide a way to exploit the short-term determinism that is present in these types of communication signals
Microcontroller-based random number generator implementation by using discrete chaotic maps
In recent decades, chaos theory has been used in different engineering applications of different disciplines. Discrete chaotic maps can be used in encryption applications for digital applications. In this study, firstly, Lozi, Tinkerbell and Barnsley Fern discrete chaotic maps are implemented based on microcontroller. Then, microcontroller based random number generator is implemented by using the three different two-dimensional discrete chaotic maps. The designed random number generator outputs are applied to NIST (National Institute of Standards and Technology) 800-22 and FIPS (Federal Information Processing Standard) tests for randomness validity. The random numbers are successful in all tests
A Triple-Memristor Hopfield Neural Network With Space Multi-Structure Attractors And Space Initial-Offset Behaviors
© 2023 IEEE. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1109/TCAD.2023.3287760Memristors have recently demonstrated great promise in constructing memristive neural networks with complex dynamics. This paper proposes a memristive Hopfield neural network with three memristive coupling synaptic weights. The complex dynamical behaviors of the triple-memristor Hopfield neural network (TM-HNN), which have never been observed in previous Hopfield-type neural networks, include space multi-structure chaotic attractors and space initial-offset coexisting behaviors. Bifurcation diagrams, Lyapunov exponents, phase portraits, Poincaré maps, and basins of attraction are used to reveal and examine the specific dynamics. Theoretical analysis and numerical simulation show that the number of space multi-structure attractors can be adjusted by changing the control parameters of the memristors, and the position of space coexisting attractors can be changed by switching the initial states of the memristors. Extreme multistability emerges as a result of the TM-HNN’s unique dynamical behaviors, making it more suitable for applications based on chaos. Moreover, a digital hardware platform is developed and the space multi-structure attractors as well as the space coexisting attractors are experimentally demonstrated. Finally, we design a pseudo-random number generator to explore the potential application of the proposed TM-HNN.Peer reviewe
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