Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices

Two generic classes of chaotic oscillators comprising four different configurations are constructed. The proposed structures are based on the simplest possible abstract models of generic second-order RC sinusoidal oscillators that satisfy the basic condition for oscillation and the frequency of oscillation formulas. By linking these sinusoidal oscillator engines to simple passive first-order or second-order nonlinear composites, chaos is generated and the evolution of the two-dimensional sinusoidal oscillator dynamics into a higher dimensional state space is clearly recognized. We further discuss three architectures into which autonomous chaotic oscillators can be decomposed. Based on one of these architectures we classify a large number of the available chaotic oscillators and propose a novel reconstruction of the classical Chua's circuit. The well-known Lorenz system of equations is also studied and a simplified model with equivalent dynamics, but containing no multipliers, is introduce

Construction of classes of circuit-independent chaotic oscillatorsusing passive-only nonlinear devices

Two generic classes of chaotic oscillators comprising four different configurations are constructed. The proposed structures are based on the simplest possible abstract models of generic second-order RC sinusoidal oscillators that satisfy the basic condition for oscillation and the frequency of oscillation formulas. By linking these sinusoidal oscillator engines to simple passive first-order or second-order nonlinear composites, chaos is generated and the evolution of the two-dimensional sinusoidal oscillator dynamics into a higher dimensional state space is clearly recognized. We further discuss three architectures into which autonomous chaotic oscillators can be decomposed. Based on one of these architectures we classify a large number of the available chaotic oscillators and propose a novel reconstruction of the classical Chua’s circuit. The well-known Lorenz system of equations is also studied and a simplified model with equivalent dynamics, but containing no multipliers, is introduced

A fully CMOS true random number generator based on hidden attractor hyperchaotic system

AbstractLow-power devices used in Internet-of-things networks have been short of security due to the high power consumption of random number generators. This paper presents a low-power hyperchaos-based true random number generator, which is highly recommended for secure communications. The proposed system, which is based on a four-dimensional chaotic system with hidden attractors and oscillators, exhibits rich dynamics. Numerical analysis is provided to verify the dynamic characteristics of the proposed system. A fully customized circuit is deployed using 130 nm CMOS technology to enable integration into low-power devices. Four output signals are used to seed a SHIFT-XOR-based chaotic data post-processing to generate random bit output. The chip prototype was simulated and tested at 100 MHz sampling frequency. The hyperchaotic circuit consumes a maximum of 980 \upmu μ W in generating chaotic signals while dissipates a static current of 623 \upmu μ A. Moreover, the proposed system provides ready-to-use binary random bit sequences which have passed the well-known statistical randomness test suite NIST SP800-22. The proposed novel system design and its circuit implementation provide a best energy efficiency of 4.37 pJ/b at a maximum sampling frequency of 100 MHz

A fully CMOS true random number generator based on hidden attractor hyperchaotic system

Low-power devices used in Internet-of-things networks have been short of security due to the high power consumption of random number generators. This paper presents a low-power hyperchaos-based true random number generator, which is highly recommended for secure communications. The proposed system, which is based on a four-dimensional chaotic system with hidden attractors and oscillators, exhibits rich dynamics. Numerical analysis is provided to verify the dynamic characteristics of the proposed system. A fully customized circuit is deployed using 130 nm CMOS technology to enable integration into low-power devices. Four output signals are used to seed a SHIFT-XOR-based chaotic data post-processing to generate random bit output. The chip prototype was simulated and tested at 100 MHz sampling frequency. The hyperchaotic circuit consumes a maximum of 980 μ W in generating chaotic signals while dissipates a static current of 623 μ A. Moreover, the proposed system provides ready-to-use binary random bit sequences which have passed the well-known statistical randomness test suite NIST SP800-22. The proposed novel system design and its circuit implementation provide a best energy efficiency of 4.37 pJ/b at a maximum sampling frequency of 100 MHz

On Bifurcations from A Four Dimensional Hysteresis Circuit Family

1つのヒステリシス素子を含む4次元自律系回路の族について考察する。この回路族の動作は、ヒステリシス的に互いに切替わる、2つの対称な3次元線形方程式で記述される。本系から2次元リターンマップ、ヤコビ行列、ヤコビアンの解析式を各々導出し、次の新結果について示す：（1）先の解析式を用いたリアプノフ指数の計算による現象の分類、（2）Period doublingによるカオスヘのルートとcrisisによるハイパーカオスヘの遷移、（3）これらの現象の基本的な分岐、（4）実装回路例の提案と回路実験による現象の一部の確認．This article discusses a four dimensional autonomous circuit family that includes one hysteresis element. The circuit family is governed by two symmetric three dimensional linear equations connected to each other by hysteresis switchings. We transform the equation into Jordan form and derive theoretical formulae of the two dimensional return map, its Jacobian matrix and its Jacobian and show the following novel results:(1) Classification of the phenomena by evaluation of Lyapunov exponents using the formulae, (2) Period doubling route to chaos and the transition to hyperchaos via crisis, (3) Basic bifurcation of these phenomena, (4) Implementation example and laboratory measurements of some attractors

A semi-systematic procedure for producing chaos from sinusoidal oscillators using diode-inductor and FET-capacitor composites

A design procedure for producing chaos is proposed. The procedure aims to transfer design issues of analog autonomous chaotic oscillators from the nonlinear domain back to the much simpler linear domain by intentionally modifying sinusoidal oscillator circuits in a semisystematic manner. Design rules that simplify this procedure are developed and then two composite devices, namely, a diode-inductor composite and a FET-capacitor composite are suggested for carrying out the modification procedure. Applications to the classical Wien-bridge oscillator are demonstrated. Experimental results, PSpice simulations, and numerical simulations of the derived models are include

Ultimate boundary estimations and topological horseshoe analysis of a new 4D hyper-chaotic system

In this paper, we first estimate the boundedness of a new proposed 4-dimensional (4D) hyper-chaotic system with complex dynamical behaviors. For this system, the ultimate bound set Ω1 and globally exponentially attractive set Ω2 are derived based on the optimization method, Lyapunov stability theory and comparison principle. Numerical simulations are presented to show the effectiveness of the method and the boundary regions. Then, to prove the existence of hyper-chaos, the hyper-chaotic dynamics of the 4D nonlinear system is investigated by means of topological horseshoe theory and numerical computation. Based on the algorithm for finding horseshoes in three-dimensional hyper-chaotic maps, we finally find a horseshoe with two-directional expansions in the 4D hyper-chaotic system, which can rigorously prove the existence of the hyper-chaos in theory

On the Application of PSpice for Localised Cloud Security

The work reported in this thesis commenced with a review of methods for creating random binary sequences for encoding data locally by the client before storing in the Cloud. The first method reviewed investigated evolutionary computing software which generated noise-producing functions from natural noise, a highly-speculative novel idea since noise is stochastic. Nevertheless, a function was created which generated noise to seed chaos oscillators which produced random binary sequences and this research led to a circuit-based one-time pad key chaos encoder for encrypting data. Circuit-based delay chaos oscillators, initialised with sampled electronic noise, were simulated in a linear circuit simulator called PSpice. Many simulation problems were encountered because of the nonlinear nature of chaos but were solved by creating new simulation parts, tools and simulation paradigms. Simulation data from a range of chaos sources was exported and analysed using Lyapunov analysis and identified two sources which produced one-time pad sequences with maximum entropy. This led to an encoding system which generated unlimited, infinitely-long period, unique random one-time pad encryption keys for plaintext data length matching. The keys were studied for maximum entropy and passed a suite of stringent internationally-accepted statistical tests for randomness. A prototype containing two delay chaos sources initialised by electronic noise was produced on a double-sided printed circuit board and produced more than 200 Mbits of OTPs. According to Vladimir Kotelnikov in 1941 and Claude Shannon in 1945, one-time pad sequences are theoretically-perfect and unbreakable, provided specific rules are adhered to. Two other techniques for generating random binary sequences were researched; a new circuit element, memristance was incorporated in a Chua chaos oscillator, and a fractional-order Lorenz chaos system with order less than three. Quantum computing will present many problems to cryptographic system security when existing systems are upgraded in the near future. The only existing encoding system that will resist cryptanalysis by this system is the unconditionally-secure one-time pad encryption

Modeling Brain Resonance Phenomena Using a Neural Mass Model

Stimulation with rhythmic light flicker (photic driving) plays an important role in the diagnosis of schizophrenia, mood disorder, migraine, and epilepsy. In particular, the adjustment of spontaneous brain rhythms to the stimulus frequency (entrainment) is used to assess the functional flexibility of the brain. We aim to gain deeper understanding of the mechanisms underlying this technique and to predict the effects of stimulus frequency and intensity. For this purpose, a modified Jansen and Rit neural mass model (NMM) of a cortical circuit is used. This mean field model has been designed to strike a balance between mathematical simplicity and biological plausibility. We reproduced the entrainment phenomenon observed in EEG during a photic driving experiment. More generally, we demonstrate that such a single area model can already yield very complex dynamics, including chaos, for biologically plausible parameter ranges. We chart the entire parameter space by means of characteristic Lyapunov spectra and Kaplan-Yorke dimension as well as time series and power spectra. Rhythmic and chaotic brain states were found virtually next to each other, such that small parameter changes can give rise to switching from one to another. Strikingly, this characteristic pattern of unpredictability generated by the model was matched to the experimental data with reasonable accuracy. These findings confirm that the NMM is a useful model of brain dynamics during photic driving. In this context, it can be used to study the mechanisms of, for example, perception and epileptic seizure generation. In particular, it enabled us to make predictions regarding the stimulus amplitude in further experiments for improving the entrainment effect

Computational Intelligence and Complexity Measures for Chaotic Information Processing

This dissertation investigates the application of computational intelligence methods in the analysis of nonlinear chaotic systems in the framework of many known and newly designed complex systems. Parallel comparisons are made between these methods. This provides insight into the difficult challenges facing nonlinear systems characterization and aids in developing a generalized algorithm in computing algorithmic complexity measures, Lyapunov exponents, information dimension and topological entropy. These metrics are implemented to characterize the dynamic patterns of discrete and continuous systems. These metrics make it possible to distinguish order from disorder in these systems. Steps required for computing Lyapunov exponents with a reorthonormalization method and a group theory approach are formalized. Procedures for implementing computational algorithms are designed and numerical results for each system are presented. The advance-time sampling technique is designed to overcome the scarcity of phase space samples and the buffer overflow problem in algorithmic complexity measure estimation in slow dynamics feedback-controlled systems. It is proved analytically and tested numerically that for a quasiperiodic system like a Fibonacci map, complexity grows logarithmically with the evolutionary length of the data block. It is concluded that a normalized algorithmic complexity measure can be used as a system classifier. This quantity turns out to be one for random sequences and a non-zero value less than one for chaotic sequences. For periodic and quasi-periodic responses, as data strings grow their normalized complexity approaches zero, while a faster deceasing rate is observed for periodic responses. Algorithmic complexity analysis is performed on a class of certain rate convolutional encoders. The degree of diffusion in random-like patterns is measured. Simulation evidence indicates that algorithmic complexity associated with a particular class of 1/n-rate code increases with the increase of the encoder constraint length. This occurs in parallel with the increase of error correcting capacity of the decoder. Comparing groups of rate-1/n convolutional encoders, it is observed that as the encoder rate decreases from 1/2 to 1/7, the encoded data sequence manifests smaller algorithmic complexity with a larger free distance value