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Chaos Engineering

Long Yunjia

Strategic Study of CAE 2001, Volume 3, Issue 2,   Pages 10-15

Abstract:

The world is nonlinear, linearity is oly its approximate description. The discovery of chaos has showed that some deterministic nonlinear systems exhibit inner random behavior. Over the past two decades, chaos was such a universal phenomenon that it was reported virtually in every scientific discipline ： mathematics, physics, chemistry, and even the social sciences. The main interest for theoretical academicians has been to investigate the essence of chaos. At the same time, practical applicatioins of chaos have been widely appreciated in many engineering fields such as information engineering, system engineering, medical engineering, agricultural engineering, electrical engineering，biological engineering, mechanical engineering, civil engineering, etc. Chaos Engineering is a new nonlinear engineering science to research the practical use of chaos and its fundamental theory. In this paper, the object, definition, concept, method, theory and application of modern Chaos Engineering are summarized. Some works done by the author and the recent advances are introduced. The fcx:us of Chaos Engineering research and development in national economy and national defense may include chaos analytic technique, chaos control technique and chaos synthetic technique.

Keywords： nonlinear     chaos     oscillation     vibration     wave    

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Road Roller Engineering Based on Chaotic Vibration Mechanics

Long Yunjia,Yang Yong,Wang Congling

Strategic Study of CAE 2000, Volume 2, Issue 9,   Pages 76-79

Abstract:

The vibration test, numerical simulation and compaction experiment of the chaotic vibratory rollers (three types： 0.75t, 101 and 14t) are completed for transform theoretical research of chaotic vibration mechanics into technology achievement in road roller engineering.

It is proved that the working efficiency of chaotic vibratory roller is 12.2% higher than that of traditional one. One type of heavy chaotic vibratory roller (14t) is used in highway development in west China.

Keywords： chaos     vibration     road roller engineering    

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Bifurcation-based fractional-order PI None

Karima RABAH, Samir LADACI, Mohamed LASHAB

Frontiers of Information Technology & Electronic Engineering 2018, Volume 19, Issue 2,   Pages 180-191 doi: 10.1631/FITEE.1601543

Abstract: We propose a novel approach called the robust fractional-order proportional-integral-derivative (FOPID) controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability analysis of the nonlinear chaotic system is made based on the proportional-integral-derivative actions using the bifurcation diagram. We extract an initial set of controller parameters, which are subsequently optimized using a quadratic criterion. The integral and derivative fractional orders are also identified by this quadratic criterion. By applying numerical simulations on two nonlinear systems, namely the multi-scroll Chen system and the Genesio-Tesi system, we show that the fractional PIλDμ controller provides the best closed-loop system performance in stabilizing the unstable fixed points, even in the presence of random perturbation.

Keywords： Fractional order system     Bifurcation diagram     Fractional PIλDμ controller     Multi-scroll Chen chaotic system     Genesio-Tesi chaotic system    

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Analysis of A Block Cipher Based on Chaos

Jin Chenhui

Strategic Study of CAE 2001, Volume 3, Issue 6,   Pages 75-80

Abstract:

In this paper, it is pointed out that the block cipher proposed in “Design of Block Cipher substitution network on chaos” can be broken by attack with known plaintext and attack with ciphertext only, and the key of this cipher can be found by the divide-and-conquer attack with the encipher transformation. Furthermore, the mutual restriction between the successive values of the chaos sequences based on the Logistic mapping, and the property that the frontal values of the chaos sequences are not sensitive to the bits on the lower po-sitions of the initial value are also pointed out.

Keywords： chaos sequence     block cipher     transposition cipher     attack with known plaintext     attack with ciphertext only     divide-and-conquer attack    

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Design of Block Cipher Substitution Network on Chaos

Sun Feng,Qin Honglei,Xu Yiaoqun,Hao Yianling

Strategic Study of CAE 2000, Volume 2, Issue 9,   Pages 47-49

Abstract:

In this paper, a design of block cipher substitution network is presented by use of the ergodic theory of chaos. The ergodic theory of chaos and the time complexity of substitution network is analyzed. The computer simulation result shows that the block cipher substitution network of chaos is highly complex and strong in anti-decipher .

Keywords： chaos sequence     permutation network     ergodic theory     time complexity    

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Differential coupling contributes to synchronization via a capacitor connection between chaotic circuits Regular Papers

Yu-meng XU, Zhao YAO, Aatef HOBINY, Jun MA

Frontiers of Information Technology & Electronic Engineering 2019, Volume 20, Issue 4,   Pages 571-583 doi: 10.1631/FITEE.1800499

Abstract:

Nonlinear oscillators and circuits can be coupled to reach synchronization and consensus. The occurrence of complete synchronization means that all oscillators can maintain the same amplitude and phase, and it is often detected between identical oscillators. However, phase synchronization means that the coupled oscillators just keep pace in oscillation even though the amplitude of each node could be different. For dimensionless dynamical systems and oscillators, the synchronization approach depends a great deal on the selection of coupling variable and type. For nonlinear circuits, a resistor is often used to bridge the connection between two or more circuits, so voltage coupling can be activated to generate feedback on the coupled circuits. In this paper, capacitor coupling is applied between two Pikovsk-Rabinovich (PR) circuits, and electric field coupling explains the potential mechanism for differential coupling. Then symmetric coupling and cross coupling are activated to detect synchronization stability, separately. It is found that resistor-based voltage coupling via a single variable can stabilize the synchronization, and the energy flow of the controller is decreased when synchronization is realized. Furthermore, by applying appropriate intensity for the coupling capacitor, synchronization is also reached and the energy flow across the coupling capacitor is helpful in regulating the dynamical behaviors of coupled circuits, which are supported by a continuous energy exchange between capacitors and the inductor. It is also confirmed that the realization of synchronization is dependent on the selection of a coupling channel. The approach and stability of complete synchronization depend on symmetric coupling, which is activated between the same variables. Cross coupling between different variables just triggers phase synchronization. The capacitor coupling can avoid energy consumption for the case with resistor coupling, and it can also enhance the energy exchange between two coupled circuits.

Keywords： Synchronization     Voltage coupling     Chaotic circuit     Capacitor coupling    

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Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications None

Saeed KHORASHADIZADEH, Mohammad-Hassan MAJIDI

Frontiers of Information Technology & Electronic Engineering 2018, Volume 19, Issue 9,   Pages 1180-1190 doi: 10.1631/FITEE.1601814

Abstract:

In this study, a new controller for chaos synchronization is proposed. It consists of a state feedback controller and a robust control term using Legendre polynomials to compensate for uncertainties. The truncation error is also considered. Due to the orthogonal functions theorem, Legendre polynomials can approximate nonlinear functions with arbitrarily small approximation errors. As a result, they can replace fuzzy systems and neural networks to estimate and compensate for uncertainties in control systems. Legendre polynomials have fewer tuning parameters than fuzzy systems and neural networks. Thus, their tuning process is simpler. Similar to the parameters of fuzzy systems, Legendre coefficients are estimated online using the adaptation rule obtained from the stability analysis. It is assumed that the master and slave systems are the Lorenz and Chen chaotic systems, respectively. In secure communication systems, observer-based synchronization is required since only one state variable of the master system is sent through the channel. The use of observer-based synchronization to obtain other state variables is discussed. Simulation results reveal the effectiveness of the proposed approach. A comparison with a fuzzy sliding mode controller shows that the proposed controller provides a superior transient response. The problem of secure communications is explained and the controller performance in secure communications is examined.

Keywords： Observer-based synchronization     Chaotic systems     Legendre polynomials     Secure communications    

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Dynamic analysis, FPGA implementation, and cryptographic application of an autonomous 5D chaotic system with offset boosting Research Articles

Sifeu Takougang Kingni, Karthikeyan Rajagopal, Serdar Çiçek, Ashokkumar Srinivasan, Anitha Karthikeyan,stkingni@gmail.com

Frontiers of Information Technology & Electronic Engineering 2020, Volume 21, Issue 6,   Pages 809-962 doi: 10.1631/FITEE.1900167

Abstract: An autonomous five-dimensional (5D) system with is constructed by modifying the well-known three-dimensional autonomous Liu and Chen system. Equilibrium points of the proposed autonomous 5D system are found and its stability is analyzed. The proposed system includes Hopf bifurcation, periodic attractors, quasi-periodic attractors, a one-scroll chaotic attractor, a double-scroll chaotic attractor, coexisting attractors, the bistability phenomenon, with partial amplitude control, reverse period-doubling, and an intermittency route to chaos. Using a field programmable gate array (FPGA), the proposed autonomous 5D system is implemented and the phase portraits are presented to check the numerical simulation results. The chaotic attractors and coexistence of the attractors generated by the of the proposed system have good qualitative agreement with those found during the numerical simulation. Finally, a sound data encryption and communication system based on the proposed autonomous 5D is designed and illustrated through a numerical example.

Keywords： 混沌系统；霍普夫分岔；共存吸引子；偏置增强；FPGA实现；声音加密    

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Chaotic dynamics of a fractional order glucose-insulin regulatory system Research Articles

Karthikeyan Rajagopal, Atiyeh Bayani, Sajad Jafari, Anitha Karthikeyan, Iqtadar Hussain,rkarthiekeyan@gmail.com,atiyeh.bayani@yahoo.com,sajad.jafari@tdtu.edu.vn,mrs.anithakarthikeyan@gmail.com,iqtadarqau@gmail.com

Frontiers of Information Technology & Electronic Engineering 2020, Volume 21, Issue 7,   Pages 1108-1118 doi: 10.1631/FITEE.1900104

Abstract: The fractional order model of a glucose-insulin regulatory system is derived and presented. It has been extensively proved in the literature that fractional order analysis of complex systems can reveal interesting and unexplored features of the system. In our investigations we have revealed that the glucose-insulin regulatory system shows and in its fractional order form. To show the effectiveness of fractional order analysis, all numerical investigations like stability of the equilibrium points, Lyapunov exponents, and plots are derived. Various biological disorders caused by an unregulated glucose-insulin system are studied in detail. This may help better understand the regulatory system.

Keywords： Diabetes mellitus     Chaos     Bifurcation     Multistability     Antimonotonicity    

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Dynamics of a neuron exposed to integer- and fractional-order discontinuous externalmagnetic flux Regular Papers

Karthikeyan RAJAGOPAL, Fahimeh NAZARIMEHR, Anitha KARTHIKEYAN, Ahmed ALSAEDI, Tasawar HAYAT, Viet-Thanh PHAM

Frontiers of Information Technology & Electronic Engineering 2019, Volume 20, Issue 4,   Pages 584-590 doi: 10.1631/FITEE.1800389

Abstract:

We propose a modified Fitzhugh-Nagumo neuron (MFNN) model. Based on this model, an integerorder MFNN system (case A) and a fractional-order MFNN system (case B) were investigated. In the presence of electromagnetic induction and radiation, memductance and induction can show a variety of distributions. Fractionalorder magnetic flux can then be considered. Indeed, a fractional-order setting can be acceptable for non-uniform diffusion. In the case of an MFNN system with integer-order discontinuous magnetic flux, the system has chaotic and non-chaotic attractors. Dynamical analysis of the system shows the birth and death of period doubling, which is a sign of antimonotonicity. Such a behavior has not been studied previously in the dynamics of neurons. In an MFNN system with fractional-order discontinuous magnetic flux, different attractors such as chaotic and periodic attractors can be observed. However, there is no sign of antimonotonicity.

Keywords： Fitzhugh-Nagumo     Chaos     Fractional order     Magnetic flux    

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Chaotic digital cryptosystem using serial peripheral interface protocol and its dsPIC implementation None

Rodrigo MÉNDEZ-RAMÍREZ, Adrian ARELLANO-DELGADO, César CRUZ-HERNÁNDEZ, Fausto ABUNDIZ-PÉREZ, Rigoberto MARTÍNEZ-CLARK

Frontiers of Information Technology & Electronic Engineering 2018, Volume 19, Issue 2,   Pages 165-179 doi: 10.1631/FITEE.1601346

Abstract: The current massive use of digital communications demands a secure link by using an embedded system (ES) with data encryption at the protocol level. The serial peripheral interface (SPI) protocol is commonly used by manufacturers of ESs and integrated circuits for applications in areas such as wired and wireless communications. We present the design and experimental implementation of a chaotic encryption and decryption algorithm applied to the SPI communication protocol. The design of the chaotic encryption algorithm along with its counterpart in the decryption is based on the chaotic Hénon map and two methods for blur and permute (in combination with DNA sequences). The SPI protocol is configured in 16 bits to synchronize a transmitter and a receiver considering a symmetric key. Results are experimentally proved using two low-cost dsPIC microcontrollers as ESs. The SPI digital-to-analog converter is used to process, acquire, and reconstruct confidential messages based on its properties for digital signal processing. Finally, security of the cryptogram is proved by a statistical test. The digital processing capacity of the algorithm is validated by dsPIC microcontrollers.

Keywords： Chaotic systems     Statistical tests     Embedded systems     dsPIC microcontroller     Serial peripheral interface (SPI) protocol    

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Pulse Transiently Chaotic Neural Network for Nonlinear Constrained Optimization

Li Ying,Cao Hongzhao,Hu Yunchang,Shang Xiuming

Strategic Study of CAE 2004, Volume 6, Issue 5,   Pages 45-48

Abstract:

Pulse Transiently Chaotic Neural Network (PTCNN) can find almost all optima including the part optima and the global with its abundance dynamical characteristic, when is used in nonlinear non-constrained optimization. The optimization problem is first unconstrained by virtue of non-differentiable exact penalty function, and is further solved by PTCNN. It is showed by an example that this method is efficient.

Keywords： PTCNN     penalty function     nonlinear constrained optimization    

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Bio-inspired cryptosystem on the reciprocal domain: DNA strands mutate to secure health data Research Articles

S. Aashiq Banu, Rengarajan Amirtharajan,aashiqbanu@sastra.ac.in,amir@ece.sastra.edu

Frontiers of Information Technology & Electronic Engineering 2021, Volume 22, Issue 7,   Pages 940-956 doi: 10.1631/FITEE.2000071

Abstract: Healthcare and telemedicine industries are relying on technology that is connected to the Internet. Digital health data are more prone to cyber attacks because of the treasure trove of personal data they possess. This necessitates protection of digital medical images and their secure transmission. In this paper, an encryption technique based on mutated with Lorenz and Lü is employed to generate high pseudo-random key streams. The proposed chaos- cryptic system operates on the integer wavelet transform (IWT) domain and a bio-inspired , unit for enhancing the confusion and diffusion phase in an approximation coefficient. Finally, an XOR operation is performed with a quantised chaotic set from the developed combined attractors. The algorithm attains an average entropy of 7.9973, near-zero correlation with an NPCR of 99.642%, a UACI of 33.438%, and a keyspace of 10. Further, the experimental analyses and NIST statistical test suite have been designed such that the proposed technique has the potency to withstand any statistical, differential, and brute force attacks.

Keywords： 医学图像加密；DNA；混沌吸引子；交叉；突变；电子医疗    

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NEHASH: high-concurrency extendible hashing for non-volatile memory Research Article

Qiankun WANG, Xingchen LI, Bingzhe WU, Ke YANG, Wei HU, Guangyu SUN, Yuchao YANG,gsun@pku.edu.cn

Frontiers of Information Technology & Electronic Engineering 2023, Volume 24, Issue 5,   Pages 731-741 doi: 10.1631/FITEE.2200463

Abstract: The problem (COP), which aims to find the optimal solution in discrete space, is fundamental in various fields. Unfortunately, many COPs are NP-complete, and require much more time to solve as the problem scale increases. Troubled by this, researchers may prefer fast methods even if they are not exact, so approximation algorithms, heuristic algorithms, and machine learning have been proposed. Some works proposed (CSA) based on the Hopfield neural network and did a good job. However, CSA is not something that current general-purpose processors can handle easily, and there is no special hardware for it. To efficiently perform CSA, we propose a software and hardware co-design. In software, we quantize the weight and output using appropriate bit widths, and then modify the calculations that are not suitable for hardware implementation. In hardware, we design a specialized hardware architecture named COPPER based on the memristor. COPPER is capable of efficiently running the modified quantized CSA algorithm and supporting the pipeline further acceleration. The results show that COPPER can perform CSA remarkably well in both speed and energy.

Keywords： Combinatorial optimization     Chaotic simulated annealing     Processing-in-memory    

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A chaotic coverage path planner for the mobilerobot based on the Chebyshev map for special missions Article

Cai-hong LI, Yong SONG, Feng-ying WANG, Zhi-qiang WANG, Yi-bin LI

Frontiers of Information Technology & Electronic Engineering 2017, Volume 18, Issue 9,   Pages 1305-1319 doi: 10.1631/FITEE.1601253

Abstract: We introduce a novel strategy of designing a chaotic coveragepath planner for the mobile robot based on the Chebyshev map for achievingspecial missions. The designed chaotic path planner consists of atwo-dimensional Chebyshev map which is constructed by two one-dimensionalChebyshev maps. The performance of the time sequences which are generatedby the planner is improved by arcsine transformation to enhance thechaotic characteristics and uniform distribution. Then the coveragerate and randomness for achieving the special missions of the robotare enhanced. The chaotic Chebyshev system is mapped into the feasibleregion of the robot workplace by affine transformation. Then a universalalgorithm of coverage path planning is designed for environments withobstacles. Simulation results show that the constructed chaotic pathplanner can avoid detection of the obstacles and the workplace boundaries,and runs safely in the feasible areas. The designed strategy is ableto satisfy the requirements of randomness, coverage, and high efficiencyfor special missions.

Keywords： Mobile robot     Chebyshev map     Chaotic     Affine transformation     Coverage path planning    

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Title Author Date Type Operation

Chaos Engineering

Long Yunjia

Journal Article

Road Roller Engineering Based on Chaotic Vibration Mechanics

Long Yunjia,Yang Yong,Wang Congling

Journal Article

Bifurcation-based fractional-order PI

Karima RABAH, Samir LADACI, Mohamed LASHAB

Journal Article

Analysis of A Block Cipher Based on Chaos

Jin Chenhui

Journal Article

Design of Block Cipher Substitution Network on Chaos

Sun Feng,Qin Honglei,Xu Yiaoqun,Hao Yianling

Journal Article

Differential coupling contributes to synchronization via a capacitor connection between chaotic circuits

Yu-meng XU, Zhao YAO, Aatef HOBINY, Jun MA

Journal Article

Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications

Saeed KHORASHADIZADEH, Mohammad-Hassan MAJIDI

Journal Article

Dynamic analysis, FPGA implementation, and cryptographic application of an autonomous 5D chaotic system with offset boosting

Sifeu Takougang Kingni, Karthikeyan Rajagopal, Serdar Çiçek, Ashokkumar Srinivasan, Anitha Karthikeyan,stkingni@gmail.com

Journal Article

Chaotic dynamics of a fractional order glucose-insulin regulatory system

Karthikeyan Rajagopal, Atiyeh Bayani, Sajad Jafari, Anitha Karthikeyan, Iqtadar Hussain,rkarthiekeyan@gmail.com,atiyeh.bayani@yahoo.com,sajad.jafari@tdtu.edu.vn,mrs.anithakarthikeyan@gmail.com,iqtadarqau@gmail.com

Journal Article

Dynamics of a neuron exposed to integer- and fractional-order discontinuous externalmagnetic flux

Karthikeyan RAJAGOPAL, Fahimeh NAZARIMEHR, Anitha KARTHIKEYAN, Ahmed ALSAEDI, Tasawar HAYAT, Viet-Thanh PHAM

Journal Article

Chaotic digital cryptosystem using serial peripheral interface protocol and its dsPIC implementation

Rodrigo MÉNDEZ-RAMÍREZ, Adrian ARELLANO-DELGADO, César CRUZ-HERNÁNDEZ, Fausto ABUNDIZ-PÉREZ, Rigoberto MARTÍNEZ-CLARK

Journal Article

Pulse Transiently Chaotic Neural Network for Nonlinear Constrained Optimization

Li Ying,Cao Hongzhao,Hu Yunchang,Shang Xiuming

Journal Article

Bio-inspired cryptosystem on the reciprocal domain: DNA strands mutate to secure health data

S. Aashiq Banu, Rengarajan Amirtharajan,aashiqbanu@sastra.ac.in,amir@ece.sastra.edu

Journal Article

NEHASH: high-concurrency extendible hashing for non-volatile memory

Qiankun WANG, Xingchen LI, Bingzhe WU, Ke YANG, Wei HU, Guangyu SUN, Yuchao YANG,gsun@pku.edu.cn

Journal Article

A chaotic coverage path planner for the mobilerobot based on the Chebyshev map for special missions

Cai-hong LI, Yong SONG, Feng-ying WANG, Zhi-qiang WANG, Yi-bin LI

Journal Article