Unexpected Behaviors in a Single Mesh Josephson Junction Based Self-Reproducing Autonomous System

2020 ◽  
Vol 30 (07) ◽  
pp. 2050097
Author(s):  
F. Calvin Talla ◽  
Robert Tchitnga ◽  
P. H. Louodop Fotso ◽  
Romanic Kengne ◽  
Bonaventure Nana ◽  
...  
Keyword(s):  
Josephson Junction ◽  
Initial Conditions ◽  
A Priori ◽  
Period Doubling ◽  
State Variables ◽  
Field Programmable ◽  
Programmable Gate Arrays ◽  
Circuit Component ◽  
Similar Class ◽  
The Stability

In the literature, existing Josephson junction based oscillators are mostly driven by external sources. Knowing the different limits of the external driven systems, we propose in this work a new autonomous one that exhibits the unusual and striking multiple phenomena among which coexist the multiple hidden attractors in self-reproducing process under the effect of initial conditions. The eight-term autonomous chaotic system has a single nonlinearity of sinusoidal type acting on only one of the state variables. A priori, the simplicity of the system does not predict the richness of its dynamics. We also find that a limit cycle attractor widens to a parameter controlling coexisting multiple-scroll attractors through the splitting and the inverse splitting of periods. Multiple types of bifurcations are found including period-doubling and period-splitting (antimonotonicity) sequences to chaos, crisis and Hopf type bifurcation. To the best of our knowledge, some of these interesting phenomena have not yet been reported in similar class of autonomous Josephson junction based circuits. Moreover, analytical investigations based on the Hopf theory analysis lead to the expressions that determine the direction of appearance of the Hopf bifurcation, confirming the existence and determining the stability of bifurcating periodic solutions. To observe this latter bifurcation and to illustrate the theoretical analysis, numerical simulations are performed. Chaos can be easily controlled by the frequency of the linear oscillator, the superconducting junction current, as well as the gain of the amplifier or circuit component values. The circuit and Field Programmable Gate Arrays (FPGA)-based implementation of the system are presented as well.

scholarly journals Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Monodromy Matrix ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Simple Expression ◽  
Buck Converter ◽  
State Variables ◽  
Bifurcation Phenomena ◽  
The Stability

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

scholarly journals Analysis of Resolution in Feedback Signals for Hardware-in-the-Loop Models of Power Converters

Electronics ◽  
2019 ◽  
Vol 8 (12) ◽  
pp. 1527
Author(s):  
María Sofía Martínez-García ◽  
Angel de Castro ◽  
Alberto Sanchez ◽  
Javier Garrido
Keyword(s):  
Power Converters ◽  
Design Criterion ◽  
Feedback Signal ◽  
Hardware In The Loop ◽  
State Variables ◽  
Gate Arrays ◽  
State Variable ◽  
Field Programmable ◽  
Programmable Gate Arrays ◽  
Optimum Width

One of the main techniques for debugging power converters is hardware-in-the-loop (HIL), which is used for real-time emulation. Field programmable gate arrays (FPGA) are the most common design platforms due to their acceleration capability. In this case, the widths of the signals have to be carefully chosen to optimize the area and speed. For this purpose, fixed-point arithmetic is one of the best options because although the design time is high, it allows the personalization of the number of bits in every signal. The representation of state variables in power converters has been previously studied, however other signals, such as feedback signals, can also have a big influence because they transmit the value of one state variable to the rest, and vice versa. This paper presents an analysis of the number of bits in the feedback signals of a boost converter, but the conclusions can be extended to other power converters. The purpose of this work is to study how many bits are necessary in order to avoid the loss of information, but also without wasting bits. Errors of the state variables are obtained with different sizes of feedback signals. These show that the errors in each state variable have similar patterns. When the number of bits increases, the error decreases down to a certain number of bits, where an almost constant error appears. However, when the bits decrease, the error increases linearly. Furthermore, the results show that there is a direct relation between the number of bits in feedback signals and the inputs of the converter in the global error. Finally, a design criterion is given to choose the optimum width for each feedback signal, without wasting bits.

scholarly journals A Fractional-Order Discrete Noninvertible Map of Cubic Type: Dynamics, Control, and Synchronization

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Xiaojun Liu ◽  
Ling Hong ◽  
Lixin Yang ◽  
Dafeng Tang
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
State Variables ◽  
Discrete Maps ◽  
The Stability ◽  
Control And Synchronization ◽  
Simultaneous Variation

In this paper, a new fractional-order discrete noninvertible map of cubic type is presented. Firstly, the stability of the equilibrium points for the map is examined. Secondly, the dynamics of the map with two different initial conditions is studied by numerical simulation when a parameter or a derivative order is varied. A series of attractors are displayed in various forms of periodic and chaotic ones. Furthermore, bifurcations with the simultaneous variation of both a parameter and the order are also analyzed in the three-dimensional space. Interior crises are found in the map as a parameter or an order varies. Thirdly, based on the stability theory of fractional-order discrete maps, a stabilization controller is proposed to control the chaos of the map and the asymptotic convergence of the state variables is determined. Finally, the synchronization between the proposed map and a fractional-order discrete Loren map is investigated. Numerical simulations are used to verify the effectiveness of the designed synchronization controllers.

scholarly journals UNIQUENESS OF BUBBLE-FREE SOLUTION IN LINEAR RATIONAL EXPECTATIONS MODELS

2003 ◽  
Vol 7 (2) ◽  
pp. 171-191 ◽  
Author(s):  
Gabriel Desgranges ◽  
Stéphane Gauthier
Keyword(s):  
Rational Expectations ◽  
Initial Conditions ◽  
Free Solution ◽  
State Variables ◽  
Minimal Set ◽  
Current State ◽  
Stable Path ◽  
Market Fundamentals ◽  
The Stability ◽  
Natural Test

One usually identifies bubble solutions to linear rational expectations models by extra components (irrelevant lags) arising in addition to market fundamentals. Although there are still many solutions relying on a minimal set of state variables, i.e., relating in equilibrium the current state of the economic system to as many lags as initial conditions, there is a conventional wisdom that the bubble-free (fundamentals) solution should be unique. This paper examines the existence of endogenous stochastic sunspot fluctuations close to solutions relying on a minimal set of state variables, which provides a natural test for identifying bubble and bubble-free solutions. It turns out that only one solution is locally immune to sunspots, independently of the stability properties of the perfect-foresight dynamics. In the standard saddle-point configuration for these dynamics, this solution corresponds to the so-called saddle stable path.

scholarly journals A Distributed Observer-Based Cyber-Attack Identification Scheme in Cooperative Networked Systems under Switching Communication Topologies

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1912
Author(s):  
Anass Taoufik ◽  
Michael Defoort ◽  
Krishna Busawon ◽  
Laurent Dala ◽  
Mohamed Djemai
Keyword(s):  
Sliding Mode ◽  
Initial Conditions ◽  
A Priori ◽  
Cyber Attacks ◽  
Consensus Algorithm ◽  
Cyber Attack ◽  
Global State ◽  
The Stability ◽  
Switching Communication Topologies ◽  
Entire Network

This paper studies an approach for detecting cyber attacks against networked cooperative systems (NCS) that are assumed to be working in a cyber-physical environment. NCS are prone to anomalies both due to cyber and physical attacks and faults. Cyber-attacks being more hazardous given the cooperative nature of the NCS may lead to disastrous consequences and thus need to be detected as soon as they occur by all systems in the network. Our approach deals with two types of malicious attacks aimed at compromising the stability of the NCS: intrusion attacks/local malfunctions on individual systems and deception/cyber-attacks on the communication between the systems. In order to detect and identify such attacks under switching communication topologies, this paper proposes a new distributed methodology that solves global state estimation of the NCS where the aim is identifying anomalies in the networked system using residuals generated by monitoring agents such that coverage of the entire network is assured. A cascade of predefined-time sliding mode switched observers is introduced for each agent to achieve a fast estimate of the global state whereby the settling time is an a priori defined parameter independently of the initial conditions. Then, using the conventional consensus algorithm, a set of residuals are generated by the agents that is capable of detecting and isolating local intrusion attacks and communication cyber-attacks in the network using only locally exchanged information. In order to prove the effectiveness of the proposed method, the framework is tested for a velocity synchronization seeking network of mobile robots.

scholarly journals A PYRAMID-BASED BLOCK OF SKEWERS FOR PIXEL PURITY INDEX FOR ENDMEMBER EXTRACTION IN HYPERSPECTRAL IMAGERY

2008 ◽  
Vol 18 (02) ◽  
pp. 469-482 ◽  
Author(s):  
CHEIN-I CHANG ◽  
MINGKAI HSUEH ◽  
WEIMIN LIU ◽  
CHAO-CHENG WU ◽  
FARZEEN CHAUDHRY ◽  
...  
Keyword(s):  
Hyperspectral Imagery ◽  
Block Design ◽  
A Priori ◽  
Block Size ◽  
Field Programmable Gate Arrays ◽  
Additional Parameter ◽  
Endmember Extraction ◽  
Gate Arrays ◽  
Field Programmable ◽  
Programmable Gate Arrays

Pixel Purity Index (PPI) has been widely used for endmember extraction. Recently, an approach using blocks of skewers was proposed by Theiler et al., called blocks of skewers (BOS) method, to improve computation of the PPI. It utilizes a block of skewers to reduce number of calculations of dot products operated by the PPI on each skewers with all data sample vectors. Unfortunately, the BOS method also suffers from the same drawbacks that the PPI does in terms of several parameters which are needed to be determined a priori. Besides, it also has an additional parameter, block size, B needed to be determined where no guideline is provided of how to select this parameter. In this paper, the BOS method is also investigated. Most importantly, a new pyramid-based block design for the BOS method is also introduced as opposed to the cube-based block designed used by Theiler et al.'s BOS. One major advantage of our proposed pyramid-based BOS over Theiler et al.'s cube-design BOS is the hardware design for Field Programmable Gate Arrays (FPGAs) implementation.

scholarly journals Phase Calibrated Ring Oscillator PUF Design and Application

Computers ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 40
Author(s):  
Wei Yan ◽  
John Chandy
Keyword(s):  
Integrated Circuits ◽  
Ring Oscillator ◽  
Key Generation ◽  
Gate Arrays ◽  
Field Programmable ◽  
Phase Calibration ◽  
Programmable Gate Arrays ◽  
Multiple Measurements ◽  
The Stability ◽  
Application Specific

A Ring Oscillator Physical Unclonable Function (RO PUF) is an application-constrained hardware security primitive that can be used for authentication and key generation. PUFs depend on variability during the fabrication process to produce random outputs that are nevertheless stable across multiple measurements. Though industry has a growing need for PUF implementations on Field Programmable Gate Arrays (FPGA) and Application-Specific Integrated Circuits (ASIC), the bit errors in PUF responses become a bottleneck and limit the usage. In this work, we comprehensively evaluate the RO PUF’s stability on FPGAs, and we propose a phase calibration process to improve the stability of RO PUFs. We also make full use of the instability of PUFs to provide a novel solution for authentication. The results show that the bit errors in our PUFs are reduced to less than 1%.

Institutional Reforms and Interaction of Local Governments

2015 ◽  
Vol 3 (2) ◽  
pp. 25-33
Author(s):  
Georges Sarafopoulos ◽  
Panagiotis G. Ioannidis
Keyword(s):  
Nash Equilibrium ◽  
Local Governments ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Replicator Dynamics ◽  
Discrete Dynamical System ◽  
Period Doubling ◽  
Box Dimension ◽  
Existence And Stability ◽  
The Stability

The paper considers the interaction between regions during the implementation of a reform, on regional development through a discrete dynamical system based on replicator dynamics. The existence and stability of equilibria of this system are studied. The authors show that the parameter of the local prosperity may change the stability of equilibrium and cause a structure to behave chaotically. For the low values of this parameter the game has a stable Nash equilibrium. Increasing these values, the Nash equilibrium becomes unstable, through period-doubling bifurcation. The complex dynamics, bifurcations and chaos are displayed by computing numerically Lyapunov numbers, sensitive dependence on initial conditions and the box dimension.

scholarly journals Complex Dynamics in a Nonlinear Cobweb Model for Real Estate Market

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Junhai Ma ◽  
Lingling Mu
Keyword(s):  
Real Estate ◽  
Demand Function ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Period Doubling ◽  
Real Estate Market ◽  
Delayed Feedback Control ◽  
Cobweb Model ◽  
Sensitive Dependence ◽  
The Stability

We establish a nonlinear real estate model based on cobweb theory, where the demand function and supply function are quadratic. The stability conditions of the equilibrium are discussed. We demonstrate that as some parameters varied, the stability of Nash equilibrium is lost through period-doubling bifurcation. The chaotic features are justified numerically via computing maximal Lyapunov exponents and sensitive dependence on initial conditions. The delayed feedback control (DFC) method is applied to control the chaos of system.

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