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The purpose of this paper is to propose a new algorithm for detection of chaos in oscillatory circuits. The algorithm is based on the wavelet transform.

The proposed detection is developed by using a specific measure obtained by averaging wavelet coefficients. This measure exhibits various values for chaotic and periodic states.

The proposed algorithm is applied to signals from autonomous systems such as the Chua’s oscillatory circuit, the Lorenz chaotic system and non-autonomous systems such as the Duffing oscillator. In addition, the detection is applied to sequences obtained from the logistic map. The results are compared to those obtained with a detrended fluctuation analysis and a time-frequency signal analysis based on detectors of chaotic states.

In this paper, a new algorithm is proposed for the detection of chaos from a single time series. The proposed technique is robust to the noise influence, having smaller calculation complexity with respect to the state-of-the-art techniques. It is suitable for real-time detection with delay that is about half of the window width.

Model-assisted probability of detection (MAPOD) is an important approach used as part of assessing the reliability of nondestructive testing systems. The purpose of this paper is to apply the polynomial chaos-based Kriging (PCK) metamodeling method to MAPOD for the first time to enable efficient uncertainty propagation, which is currently a major bottleneck when using accurate physics-based models.

In this paper, the state-of-the-art Kriging, polynomial chaos expansions (PCE) and PCK are applied to “a^ vs a”-based MAPOD of ultrasonic testing (UT) benchmark problems. In particular, Kriging interpolation matches the observations well, while PCE is capable of capturing the global trend accurately. The proposed UP approach for MAPOD using PCK adopts the PCE bases as the trend function of the universal Kriging model, aiming at combining advantages of both metamodels.

To reach a pre-set accuracy threshold, the PCK method requires 50 per cent fewer training points than the PCE method, and around one order of magnitude fewer than Kriging for the test cases considered. The relative differences on the key MAPOD metrics compared with those from the physics-based models are controlled within 1 per cent.

The contributions of this work are the first application of PCK metamodel for MAPOD analysis, the first comparison between PCK with the current state-of-the-art metamodels for MAPOD and new MAPOD results for the UT benchmark cases.

This study aims to provide a new method of multiscale directional Lyapunov exponents (MSDLE) calculated based on the state space reconstruction for the nonstationary time series, which can be applied to detect the small target covered by sea clutter.

Reconstructed state space is divided into non-overlapping submatrices whose columns are equal to a predetermined scale. The authors compute eigenvalues and eigenvectors of the covariance matrix of each submatrix and extract the principal components σ_ip and their corresponding eigenvectors. Then, the angles ψ_ip of eigenvectors between two successive submatrices were calculated. The curves of (σ_ip, ψ_ip) reflect the nonlinear dynamics both in kinetic and directional and form a spectrum with multiscale. The fluctuations of (σ_ip, ψ_ip), which are sensitive to the differences of backscatter between sea wave and target, are taken out as the features for the target detection.

The proposed method can reflect the local dynamics of sea clutter and the small target within sea clutter is easily detected. The test on the ice multiparameter imaging X-ban radar data and the comparison to K distribution based method illustrate the effectiveness of the proposed method.

The detection of a small target in sea clutter is a compelling issue, as the conventional statistical models cannot well describe the sea clutter on a larger timescale, and the methods based on statistics usually require the stationary sea clutter. It has been proven that sea clutter is nonlinear, nonstationary or cyclostationary and chaotic. The new method of MSDLE proposed in the paper can effectively and efficiently detect the small target covered by sea clutter, which can be also introduced and applied to military, aerospace and maritime fields.

The purpose of this paper is to investigate the nonlinear dynamics of the aircraft assembly lines. An approach for modeling and analyzing the production rate of an aircraft assembly line is introduced using the chaos theory.

First, two key system variables including reliability and learning ability are considered to control the dynamics model. The discrete-time dynamics equation of the production rate is established as a function of the reliability and the learning rate. Then an improved Gauss-learning curve is proposed and applied to aircraft assembling condition. Finally, the bifurcation diagrams and the maximal Lyapunov exponents are used and applied to the experimental study to analyze the dynamic behavior under different combinations of parameters.

On the basis of the experimental study, it is shown that chaotic behavior really exists in the aircraft assembly lines. The reliability and the Gauss-learning curve can nonlinearly affect the production rate.

This paper applied nonlinear dynamics and chaotic theory to the production analyses of the aircraft assembly lines for the first time. The proposed model has been successfully applied to a practical case, and the result justifies its advantage as well as feasibility to both theory and engineering application.

The problem of manufacturer-customer relationships is becoming the key factor of enterprise development, and the contradiction between manufacturer’s objective and customer’s satisfaction still exists. Customers claim for product safety from manufacturers, so manufacturers should take corporate social responsibility (CSR) into their company philosophy or even enhance the degree of CSR during their production. The purpose of this paper is to investigate the influences of parameters on the stability of risk-averse complementary product manufacturers.

In this study, three dynamic game models are developed: manufacturer 1 – leader Stackelberg game model, manufacturer 2 – leader Stackelberg game model and Nash game model. Using bifurcation diagrams, the largest Lyapunov exponent, 0-1 test for chaos and parameter basin plots, the influences of parameters on the complex behaviors of the three models are analyzed.

The authors demonstrate that the system exists in deterministic chaos when the parameter exceeds a certain value. The lead manufacturer will not be a beneficiary in chaotic state, and when two manufacturers have the same status the stability of the system weakens, which renders it easily chaotic.

In this paper, the authors make some assumptions, which when applied broadly could lead to some findings.

The authors find that the lead manufacturer will derive the greatest profit and will exert the least effort compared with the follower manufacturer, but that both manufacturers will exert greater effort in the Nash game. The two manufacturers should be cautious while selecting the parameter ' s value so that the stability of the system is maintained.

The research will serve as a guide for the two complementary manufacturers in their decision-making process.

The originality and value of the research rest on the use of dynamic thinking in ensuring stability in the quality of complementary products considering the firms’ market powers. The research will serve as a guide for the two complementary manufacturers in their decision-making process.

This paper aims to explain, first of all, signal modeling steps using Poincaré, and then considering the occurred events, concept of information applying Poincaré section and information approach, the brain pattern variations in autism spectrum disorder (ASD) cases will be diagnosed. A kind of representation of electroencephalogram (EEG) signal, namely, complementary plot, in which the main characteristic is special attention to asymmetry and symmetry coexist in natural and human processes, is introduced. In this paper, a new model is provided whose variations of patterns are similar to EEG’s when the transformation parameter is changed. A significant difference between ASD and healthy cases was also observed, which could be used to distinguish between various types of systems.

Complementary plot method is one of the most proper representations for Poincaré section of complex dynamics, because, as it was said about its characteristics, it has a qualitative approach toward signal (Sabelli, 2000, 2001, 2003, 2008, 2005, Sabelli et al., 2011). Considering the special conditions of this representation, here, intersection with a circle y² + x² = r² will be used; the important fact is, on the contrary to previous representations in which circular section had energy concept, here circular section considers phases. For finding trajectory intersection points, after calculating the sin and cosine of each term of EEG, plotting them in XY plane and drawing a chord between successive points of presentation transitions, then its intersections with the assumed circle are determined. But considering the sampling frequency, chords and Poincaré section, in this space, a minimum error – as the threshold – should be assumed in the program.

Natural and human processes are biotic (life-like) and creative (Sabelli and Galilei), and studying coexisting opposites by calculating the sine and cosine of each term in heartbeat intervals, weather variables and integer biotic series or random walk reveals an astonishingly regular mandala pattern; these patterns are not generated by random, periodic or chaotic series (Sabelli, 2005). This paper shows that in EEG of ASD children, mandala-like patterns of concentric rings are emergent in all situations (baseline – watching animation with voice and without voice) and electrode site (C3 and C4), but not in healthy individuals. The authors take the relation between sine and cosine functions as a mathematical model for complementary opposition, because it involves reciprocity and orthogonality sine and cosine are natural models for information. In fact, trigonometric analyses of empirical data to be described in this paper suggest expanding the concept of co-creative opposition to include uncorrelated opposites and partial opposites, i.e. partial agonists and partial antagonists that are neither linear nor orthogonal. Using Poincaré sections, it is shown that the difference in information and creativity of the data is the distinctive characteristic in ASD and healthy cases. Creation is the generation of novelty, diversity and complexity in complex systems.

This paper is an original paper based on cybernetic approaches for studying the variations of ASD children.