Modern software-based services are implemented as distributed systems with complex behavior and failure modes. Many large tech organizations are using experimentation to verify such systems' ...reliability. Netflix engineers call this approach chaos engineering. They've determined several principles underlying it and have used it to run experiments. This article is part of a theme issue on DevOps.
Recent developments in engineering applications of stochastic resonance have expanded to various fields, especially biomedicine. Deterministic chaos generates a phenomenon known as chaotic resonance, ...which is similar to stochastic resonance. However, engineering applications of chaotic resonance are limited owing to the problems in controlling chaos, despite its uniquely high sensitivity to weak signal responses. To tackle these problems, a previous study proposed “reduced region of orbit” (RRO) feedback methods, which cause chaotic resonance using external feedback signals. However, this evaluation was conducted under noise-free conditions. In actual environments, background noise and measurement errors are inevitable in the estimation of RRO feedback strength; therefore, their impact must be elucidated for the application of RRO feedback methods. In this study, we evaluated the chaotic resonance induced by the RRO feedback method in chaotic neural systems in the presence of stochastic noise. Specifically, we focused on the chaotic resonance induced by RRO feedback signals in a neural system composed of excitatory and inhibitory neurons, a typical neural system wherein chaotic resonance is observed in the presence of additive noise and feedback signals including the measurement error (called contaminant noise). It was found that for a relatively small noise strength, both types of noise commonly degenerated the degree of synchronization in chaotic resonance induced by RRO feedback signals, although these characteristics were significantly different. In contrast, chaos-chaos intermittency synchronization was observed for a relatively high noise strength owing to the noise-induced attractor merging bifurcation for both types of noise. In practical neural systems, the influence of noise is unavoidable; therefore, this study highlighted the importance of the countermeasures for noise in the application of chaotic resonance and utilization of noise-induced attractor merging bifurcation.
Replication of chaos Akhmet, M.U.; Fen, M.O.
Communications in nonlinear science & numerical simulation,
October 2013, 2013-10-00, 20131001, Letnik:
18, Številka:
10
Journal Article
Recenzirano
Odprti dostop
► Replication of chaos in continuous-time dynamics is introduced. ► Hyperbolic and chaotic sets of functions are defined. ► The extension is rigorously approved for Devaney and Li-Yorke chaos. ► ...Simulations of attractors, bifurcation diagrams illustrate the results. ► Discussions of future investigations are provided.
We propose a rigorous method for replication of chaos from a prior one to systems with large dimensions. Extension of the formal properties and features of a complex motion can be observed such that ingredients of chaos united as known types of chaos, Devaney’s, Li-Yorke and obtained through period-doubling cascade. This is true for other appearances of chaos: intermittency, structure of the chaotic attractor, its fractal dimension, form of the bifurcation diagram, the spectra of Lyapunov exponents, etc. That is why we identify the extension of chaos through the replication as morphogenesis.
To provide rigorous study of the subject, we introduce new definitions such as chaotic sets of functions, the generator and replicator of chaos, and precise description of ingredients for Devaney and Li-Yorke chaos in continuous dynamics. Appropriate simulations which illustrate the chaos replication phenomenon are provided. Moreover, in discussion form we consider inheritance of intermittency, replication of Shil’nikov orbits and quasiperiodical motions as a possible skeleton of a chaotic attractor. Chaos extension in an open chain of Chua circuits is also demonstrated.
Data rate and energy efficiency decrement caused by the transmission of reference and data carrier signals in equal portions constitute the major drawback of differential chaos shift keying (DCSK) ...systems. To overcome this dominant drawback, a short reference DCSK system (SR-DCSK) is proposed. In SRDCSK, the number of chaotic samples that constitute the reference signal is shortened to R such that it occupies less than half of the bit duration. To build the transmitted data signal, P concatenated replicas of R are used to spread the data. This operation increases data rate and enhances energy efficiency without imposing extra complexity onto the system structure. The receiver uses its knowledge of the integers R and P to recover the data. The proposed system is analytically studied and the enhanced data rate and bit energy saving percentages are computed. Furthermore, theoretical performance for AWGN and multipath fading channels are derived and validated via simulation. In addition, optimising the length of the reference signal R is exposed to detailed discussion and analysis. Finally, the application of the proposed short reference technique to the majority of transmit reference systems such as DCSK, multicarrier DCSK, and quadratic chaos shift keying enhances the overall performance of this class of chaotic modulations and is, therefore, promising.
In this paper, firstly, we investigate a new 1D PWLCM-Sin (PS) map which derived from PWLCM and Sin map by modulo operation. Due to the stronger parameter space, bigger Lyapunov exponents and better ...ergodicity than simple 1D map, the PS map is more suitable for local map of spatiotemporal dynamics. Secondly, with the novel 2D pseudo-random mixed coupling method we present a spatiotemporal chaos which used PS map as local map
f
(
x
). This spatiotemporal chaos named 2D Mixed pseudo-random Coupling PS Map Lattice (2DMCPML). The experimental results of bifurcation diagrams, Kolmogorov–Sinai entropy density and spatiotemporal chaotic diagrams showed that 2DMCPML has advantages of larger parameter space, more complex chaotic behavior and more ergodic output sequence than CML. Therefore, 2DMCPML is more suitable in cryptography than CML. Subsequently, we proposed a chaos-based random S-box design algorithm employed the spatial chaotic character of 2DMCPML to generate a large number of S-boxes. The cryptographic performance indicated that generated S-boxes can resist cryptanalysis attack well. Finally, four criteria bounds are set. The numbers of S-boxes satisfying these bounds generated by 2DMCPML and several 1D chaotic maps is calculated, respectively. The result showed that spatiotemporal chaos can generate more S-boxes with high cryptographic quality than low-dimensional chaos. This new discovery is significant to the development of some cryptographic researches such as dynamic S-box algorithm.
This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is ...introduced as a natural extension of ideas from quantum chaos and random matrix theory (RMT). To this end, we present a brief overview of classical and quantum chaos, as well as RMT and some of its most important predictions. The latter include the statistics of energy levels, eigenstate components, and matrix elements of observables. Building on these, we introduce the ETH and show that it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath. We examine numerical evidence of eigenstate thermalization from studies of many-body lattice systems. We also introduce the concept of a quench as a means of taking isolated systems out of equilibrium, and discuss results of numerical experiments on quantum quenches. The second part of the review explores the implications of quantum chaos and ETH to thermodynamics. Basic thermodynamic relations are derived, including the second law of thermodynamics, the fundamental thermodynamic relation, fluctuation theorems, the fluctuation-dissipation relation, and the Einstein and Onsager relations. In particular, it is shown that quantum chaos allows one to prove these relations for individual Hamiltonian eigenstates and thus extend them to arbitrary stationary statistical ensembles. In some cases, it is possible to extend their regimes of applicability beyond the standard thermal equilibrium domain. We then show how one can use these relations to obtain nontrivial universal energy distributions in continuously driven systems. At the end of the review, we briefly discuss the relaxation dynamics and description after relaxation of integrable quantum systems, for which ETH is violated. We present results from numerical experiments and analytical studies of quantum quenches at integrability. We introduce the concept of the generalized Gibbs ensemble and discuss its connection with ideas of prethermalization in weakly interacting systems.
Using methods of entropy in ergodic theory, we prove that positive topological entropy implies chaos DC2. That is, if a system (X, T) has positive topological entropy, then there exists an ...uncountable set E such that for any two distinct points x, y in E, $\begin{matrix} lim inf \ \\ n\rightarrow \infty \ \end{matrix} \frac {1}{n}\sum_{i=1}^{n} dist (T ^i x, T^i y)=0$ and $\begin{matrix} lim sup \ \\ n\rightarrow \infty \ \end{matrix} \frac {1}{n}\sum_{i=1}^{n} dist (T ^i x, T^i y)> 0$.
Polynomial Chaos (PC) expansions are widely used in various engineering fields for quantifying uncertainties arising from uncertain parameters. The computational cost of classical PC solution schemes ...is unaffordable as the number of deterministic simulations to be calculated grows dramatically with the number of stochastic dimension. This considerably restricts the practical use of PC at the industrial level. A common approach to address such problems is to make use of sparse PC expansions. This paper presents a non-intrusive regression-based method for building sparse PC expansions. The most important PC contributions are detected sequentially through an automatic search procedure. The variable selection criterion is based on efficient tools relevant to probabilistic method. Two benchmark analytical functions are used to validate the proposed algorithm. The computational efficiency of the method is then illustrated by a more realistic CFD application, consisting of the non-deterministic flow around a transonic airfoil subject to geometrical uncertainties. To assess the performance of the developed methodology, a detailed comparison is made with the well established LAR-based selection technique. The results show that the developed sparse regression technique is able to identify the most significant PC contributions describing the problem. Moreover, the most important stochastic features are captured at a reduced computational cost compared to the LAR method. The results also demonstrate the superior robustness of the method by repeating the analyses using random experimental designs.
This paper initiates a systematic methodology for real-time chaos-based video encryption and decryption communications on the system design and algorithm analysis. The proposed system design and ...algorithm analysis have been validated on an FPGA hardware platform via Verilog Hardware Description Language (Verilog HDL). Based on the fundamental anti-control principles of dynamical systems, a 6-D real domain chaotic system is designed, and then the corresponding Verilog HDL algorithm is developed. The proposed Verilog HDL algorithm is utilized to design a real-time chaos-based secure video communication system, with a generalized design principle derived, which is implemented on an FPGA hardware platform equipped with an XUP Virtex-II chip. Following this line, the designed working mechanism is demonstrated by hardware experiments. The security performance is tested using the TESTU01 statistical test suites, the differential analysis, and the sensitivity of key parameters mismatch. Both theoretical analysis and experimental results validate the feasibility and reliability of the proposed system.
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space ...trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order.The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. Ivo Petrá is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Koice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.
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