Dynamics of a New Multi-Cavity Hyperchaotic Map and Its DSP Implementation

2019 ◽  
Vol 29 (14) ◽  
pp. 1950194
Author(s):  
Yan Xiao ◽  
Kehui Sun ◽  
Mengyao Yu ◽  
Xuemei Xu
Keyword(s):  
Secure Communication ◽  
Closed Loop ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Maximum Lyapunov Exponent ◽  
Dynamical Characteristics ◽  
Dynamical Behaviors ◽  
Higher Dimensional ◽  
Large Maximum ◽  
Chaotic Secure Communication

A new higher-dimensional hyperchaotic map, named Sine Chebyshev modulation map (SCMM), is proposed based on the closed-loop modulation coupling (CMC) model. The dynamics of the SCMM are evaluated by attractor diagrams, Lyapunov exponents and bifurcations. By designing a piecewise-linear function, the SCMM is expanded to the grid multi-cavity form. Dynamical behaviors of the two-dimensional grid multi-cavity SCMM are then analyzed. The results show that it has rich dynamical characteristics, including complicated phase space trajectories, hyperchaotic behaviors, large maximum Lyapunov exponent and typical bifurcations. The complexity of the new grid multi-cavity hyperchaotic map is large in the entire parameter space. Finally, digital circuits of 2D-SCMM and 2D grid multi-cavity SCMM are implemented based on the DSP technique. The feasibility of the circuit is verified, and it lays the foundation for applications in chaotic secure communication.

scholarly journals PVT-Robust CMOS Programmable Chaotic Oscillator: Synchronization of Two 7-Scroll Attractors

Electronics ◽  
2018 ◽  
Vol 7 (10) ◽  
pp. 252 ◽  
Author(s):  
Victor Carbajal-Gomez ◽  
Esteban Tlelo-Cuautle ◽  
Carlos Sanchez-Lopez ◽  
Francisco Fernandez-Fernandez
Keyword(s):  
Integrated Circuit ◽  
Secure Communication ◽  
Piecewise Linear ◽  
Cmos Technology ◽  
Oxide Semiconductor ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Maximum Lyapunov Exponent ◽  
Chaotic Oscillators ◽  
Cmos Integrated Circuit

Designing chaotic oscillators using complementary metal-oxide-semiconductor (CMOS) integrated circuit technology for generating multi-scroll attractors has been a challenge. That way, we introduce a current-mode piecewise-linear (PWL) function based on CMOS cells that allow programmable generation of 2–7-scroll chaotic attractors. The mathematical model of the chaotic oscillator designed herein has four coefficients and a PWL function, which can be varied to provide a high value of the maximum Lyapunov exponent. The coefficients are implemented electronically by designing operational transconductance amplifiers that allow programmability of their transconductances. Design simulations of the chaotic oscillator are provided for the 0.35 μ m CMOS technology. Post-layout and process–voltage–temperature (PVT) variation simulations demonstrate robustness of the multi-scroll chaotic attractors. Finally, we highlight the synchronization of two seven-scroll attractors in a master–slave topology by generalized Hamiltonian forms and observer approach. Simulation results show that the synchronized CMOS chaotic oscillators are robust to PVT variations and are suitable for chaotic secure communication applications.

scholarly journals Characteristic Analysis of Fractional-Order 4D Hyperchaotic Memristive Circuit

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Jun Mou ◽  
Kehui Sun ◽  
Huihai Wang ◽  
Jingya Ruan
Keyword(s):  
Fractional Order ◽  
Secure Communication ◽  
System Parameter ◽  
Phase Portraits ◽  
Spectral Entropy ◽  
Characteristic Analysis ◽  
Dynamical Characteristics ◽  
Dynamical Behaviors ◽  
Adomian Decomposition ◽  
Memristive Circuit

Dynamical behaviors of the 4D hyperchaotic memristive circuit are analyzed with the system parameter. Based on the definitions of fractional-order differential and Adomian decomposition algorithm, the numerical solution of fractional-order 4D hyperchaotic memristive circuit is investigated. The distribution of stable and unstable regions of the fractional-order 4D hyperchaotic memristive circuit is determined, and dynamical characteristics are studied by phase portraits, Lyapunov exponents spectrum, and bifurcation diagram. Complexities are calculated by employing the spectral entropy (SE) algorithm and C0 algorithm. Complexity results are consistent with that of the bifurcation diagrams, and this means that complexity can also reflect the dynamic characteristics of a chaotic system. Results of this paper provide a theoretical and experimental basis for the application of fractional-order 4D hyperchaotic memristive circuit in the field of encryption and secure communication.

A MODIFIED CHUA'S CIRCUIT WITH AN ATTRACTION-REPULSION FUNCTION

2008 ◽  
Vol 18 (07) ◽  
pp. 1865-1888 ◽  
Author(s):  
RONG LI ◽  
ZHISHENG DUAN ◽  
BO WANG ◽  
GUANRONG CHEN
Keyword(s):  
Computer Simulations ◽  
Piecewise Linear ◽  
Nonlinear Function ◽  
Piecewise Linear Function ◽  
Stability Conditions ◽  
Chua’S Circuit ◽  
Bifurcation Diagrams ◽  
Chua's Circuit ◽  
Dynamical Behaviors ◽  
New System

In this paper, the original Chua's circuit is modified by substituting its piecewise-linear function with an attraction-repulsion function. Some new complex dynamical behaviors such as chaos are observed through computer simulations. Basic properties of the new circuit are analyzed by means of bifurcation diagrams. Lagrange stability conditions of the circuit are derived. A comparison between this modified Chua's circuit with an attraction-repulsion function and the modified Chua's circuit with a cubic nonlinear function is presented. Moreover, a generalization of the new circuit that can generate multiple scrolls is designed and simulated. Finally, a physical circuit is built to visualize the new system, with some experimental observations reported.

scholarly journals MINLP formulations for continuous piecewise linear function fitting

2021 ◽  
Author(s):  
Noam Goldberg ◽  
Steffen Rebennack ◽  
Youngdae Kim ◽  
Vitaliy Krasko ◽  
Sven Leyffer
Keyword(s):  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Mixed Integer ◽  
Function Fitting ◽  
Computational Performance ◽  
Integer Nonlinear Programming ◽  
Minlp Model ◽  
Necessary Constraints ◽  
Continuous Piecewise Linear Function

AbstractWe consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

scholarly journals A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Hamid Reza Erfanian ◽  
M. H. Noori Skandari ◽  
A. V. Kamyad
Keyword(s):  
Nonsmooth Optimization ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Piecewise Linear Function ◽  
Nonsmooth Equations ◽  
Smooth Functions ◽  
Generalized Derivative ◽  
Novel Approach

We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other words, nonsmooth function is approximated by a piecewise linear function based on generalized derivative. In the next step, we solve smooth linear optimization problem whose optimal solution is an approximate solution of main problem. Then, we apply the results for solving system of nonsmooth equations. Finally, for efficiency of our approach some numerical examples have been presented.

CHUA’S CIRCUIT: AN OVERVIEW TEN YEARS LATER

1994 ◽  
Vol 04 (02) ◽  
pp. 117-159 ◽  
Author(s):  
LEON O. CHUA
Keyword(s):  
Secure Communication ◽  
Vector Fields ◽  
Piecewise Linear ◽  
International Workshop ◽  
Noise Spectrum ◽  
Chaotic Regime ◽  
Practical Significance ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
New Phenomena

More than 200 papers, two special issues (Journal of Circuits, Systems, and Computers, March, June, 1993, and IEEE Trans. on Circuits and Systems, vol. 40, no. 10, October, 1993), an International Workshop on Chua’s Circuit: chaotic phenomena and applica tions at NOLTA’93, and a book (edited by R.N. Madan, World Scientific, 1993) on Chua’s circuit have been published since its inception a decade ago. This review paper attempts to present an overview of these timely publications, almost all within the last six months, and to identify four milestones of this very active research area. An important milestone is the recent fabrication of a monolithic Chua’s circuit. The robustness of this IC chip demonstrates that an array of Chua’s circuits can also be fabricated into a monolithic chip, thereby opening the floodgate to many unconventional applications in information technology, synergetics, and even music. The second milestone is the recent global unfolding of Chua’s circuit, obtained by adding a linear resistor in series with the inductor to obtain a canonical Chua’s circuit— now generally referred to as Chua’s oscillator. This circuit is most significant because it is structurally the simplest (it contains only 6 circuit elements) but dynamically the most complex among all nonlinear circuits and systems described by a 21-parameter family of continuous odd-symmetric piecewise-linear vector fields. The third milestone is the recent discovery of several important new phenomena in Chua’s circuits, e.g., stochastic resonance, chaos-chaos type intermittency, 1/f noise spectrum, etc. These new phenomena could have far-reaching theoretical and practical significance. The fourth milestone is the theoretical and experimental demonstration that Chua’s circuit can be easily controlled from a chaotic regime to a prescribed periodic or constant orbit, or it can be synchronized with 2 or more identical Chua’s circuits, operating in an oscillatory, or a chaotic regime. These recent breakthroughs have ushered in a new era where chaos is deliberately created and exploited for unconventional applications, e.g. secure communication.

scholarly journals DESIGN OF TIME DELAYED CHAOTIC CIRCUIT WITH THRESHOLD CONTROLLER

2011 ◽  
Vol 21 (03) ◽  
pp. 725-735 ◽  
Author(s):  
K. SRINIVASAN ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
M. LAKSHMANAN ◽  
SUDESHNA SINHA
Keyword(s):  
Numerical Simulations ◽  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operational Amplifiers ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Threshold Values ◽  
Chaotic Circuit

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

High transparency flexible sensor for pressure and proximity sensing

2018 ◽  
Vol 32 (32) ◽  
pp. 1850394 ◽  
Author(s):  
Dan Bu ◽  
Si Qi Li ◽  
Yun Ming Sang ◽  
Cheng Jun Qiu
Keyword(s):  
Indium Tin Oxide ◽  
Pressure Range ◽  
Piecewise Linear ◽  
High Sensitivity ◽  
Maximum Error ◽  
Piecewise Linear Function ◽  
Good Repeatability ◽  
Flexible Pressure Sensor ◽  
Human Finger ◽  
Proximity Sensing

A high-sensitivity and high-transmittance flexible pressure sensor is presented in this paper. Using polydimethylsiloxane (PDMS) sensing film to cover indium tin oxide (ITO) electrodes interdigitated on the polyethylene terephthalate (PET) substrate, an interdigital capacitance (IDC) structure is constructed. The pressure and proximity sensing characteristics of the fabricated IDC sensor are investigated. The experiment results show that the IDC sensor has the piecewise linear function in different pressure range, especially sensitive to the low-pressure range with the pressure sensitivity of 6.64 kPa[Formula: see text]. Moreover, it has a good repeatability with the maximum error rate of 2.73% and a high transmittance over 90% in the wavelength range from 400 nm to 800 nm. As a human finger approaches or leaves, the proximity sensing characteristic emerges, with a maximum sensing distance of about 20 cm.

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