Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Research on digital image watermark encryption based on hyperchaos

The digital watermarking technique embeds meaningful information into one or more watermark images hidden in one image, in which it is known as a secret carrier. It is difficult for a hacker to extract or remove any hidden watermark from an image, and especially to crack so called digital watermark. The combination of digital watermarking technique and traditional image encryption technique is able to greatly improve anti-hacking capability, which suggests it is a good method for keeping the integrity of the original image. The research works contained in this thesis include: (1)A literature review the hyperchaotic watermarking technique is relatively more advantageous, and becomes the main subject in this programme. (2)The theoretical foundation of watermarking technologies, including the human visual system (HVS), the colour space transform, discrete wavelet transform (DWT), the main watermark embedding algorithms, and the mainstream methods for improving watermark robustness and for evaluating watermark embedding performance. (3) The devised hyperchaotic scrambling technique it has been applied to colour image watermark that helps to improve the image encryption and anti-cracking capabilities. The experiments in this research prove the robustness and some other advantages of the invented technique. This thesis focuses on combining the chaotic scrambling and wavelet watermark embedding to achieve a hyperchaotic digital watermark to encrypt digital products, with the human visual system (HVS) and other factors taken into account. This research is of significant importance and has industrial application value

Entropy in Image Analysis III

Image analysis can be applied to rich and assorted scenarios; therefore, the aim of this recent research field is not only to mimic the human vision system. Image analysis is the main methods that computers are using today, and there is body of knowledge that they will be able to manage in a totally unsupervised manner in future, thanks to their artificial intelligence. The articles published in the book clearly show such a future

Entropy in Image Analysis II

Image analysis is a fundamental task for any application where extracting information from images is required. The analysis requires highly sophisticated numerical and analytical methods, particularly for those applications in medicine, security, and other fields where the results of the processing consist of data of vital importance. This fact is evident from all the articles composing the Special Issue "Entropy in Image Analysis II", in which the authors used widely tested methods to verify their results. In the process of reading the present volume, the reader will appreciate the richness of their methods and applications, in particular for medical imaging and image security, and a remarkable cross-fertilization among the proposed research areas

Design and Implementation of Secure Chaotic Communication Systems

Chaotic systems have properties such as ergodicity, sensitivity to initial conditions/parameter mismatches, mixing property, deterministic dynamics, structure complexity, to mention a few, that map nicely with cryptographic requirements such as confusion, diffusion, deterministic pseudorandomness, algorithm complexity. Furthermore, the possibility of chaotic synchronization, where the master system (transmitter) is driving the slave system (receiver) by its output signal, made it probable for the possible utilization of chaotic systems to implement security in the communication systems. Many methods like chaotic masking, chaotic modulation, inclusion, chaotic shift keying (CSK) had been proposed however, many attack methods later showed them to be insecure. Different modifications of these methods also exist in the literature to improve the security, but almost all suffer from the same drawback. Therefore, the implementation of chaotic systems in security still remains a challenge. In this work, different possibilities on how it might be possible to improve the security of the existing methods are explored. The main problem with the existing methods is that the message imprint could be found in the dynamics of the transmitted signal, therefore by some signal processing or pattern classification techniques, etc, allow the exposition of the hidden message. Therefore, the challenge is to remove any pattern or change in dynamics that the message might bring in the transmitted signal

Modelling, Monitoring, Control and Optimization for Complex Industrial Processes

This reprint includes 22 research papers and an editorial, collected from the Special Issue "Modelling, Monitoring, Control and Optimization for Complex Industrial Processes", highlighting recent research advances and emerging research directions in complex industrial processes. This reprint aims to promote the research field and benefit the readers from both academic communities and industrial sectors

Design and implementation of secure chaotic communication systems

Chaotic systems have properties such as ergodicity, sensitivity to initial conditions/parameter mismatches, mixing property, deterministic dynamics, structure complexity, to mention a few, that map nicely with cryptographic requirements such as confusion, diffusion, deterministic pseudorandomness, algorithm complexity. Furthermore, the possibility of chaotic synchronization, where the master system (transmitter) is driving the slave system (receiver) by its output signal, made it probable for the possible utilization of chaotic systems to implement security in the communication systems. Many methods like chaotic masking, chaotic modulation, inclusion, chaotic shift keying (CSK) had been proposed however, many attack methods later showed them to be insecure. Different modifications of these methods also exist in the literature to improve the security, but almost all suffer from the same drawback. Therefore, the implementation of chaotic systems in security still remains a challenge. In this work, different possibilities on how it might be possible to improve the security of the existing methods are explored. The main problem with the existing methods is that the message imprint could be found in the dynamics of the transmitted signal, therefore by some signal processing or pattern classification techniques, etc, allow the exposition of the hidden message. Therefore, the challenge is to remove any pattern or change in dynamics that the message might bring in the transmitted signal.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Recurrence network analysis of EEG signals: A Geometric Approach

Understanding the neuronal dynamics of dynamical diseases like epilepsy is of fundamental importance. For instance, establishing the presence of deterministic chaos can open up possibilities that can lead to potential medical applications, including timely prevention of seizures. Additionally, understanding the dynamics of interictal activity can greatly aid the localization of epileptic foci without the need for recording seizures. Recurrences, a fundamental property of dynamical systems, are useful for characterizing nonlinear systems. Recurrence networks, which are obtained by reinterpreting the recurrence matrix as an adjacency matrix of a complex network, are useful in characterizing the structural or geometric properties of the underlying system. Recurrence network analysis has established itself as a versatile tool in the field of nonlinear time series analysis and its applicability in investigating neural dynamics remains unexplored. Certain recurrence network measures are particularly sensitive to the presence of unstable periodic orbits (UPOs), which are important for detecting determinism and are the backbone of chaotic attractors.In this thesis, we introduce recurrence network analysis as a tool for nonlinear time series analysis of epileptic electroencephalographic (EEG) signals. We present novel results based on the application of recurrence network analysis combined with surrogate testing to intracranial and extracranial epileptic EEG signals. In addition, using paradigmatic examples of dynamical systems, we present theoretical results exploring the effect of increasing noise levels on recurrence network measures.Using paradigmatic model systems, we first demonstrate that recurrence network measures can distinguish between deterministic (chaos) and stochastic processes, even at short data lengths (≈ 200 samples). In particular, our results from theoretical simulations show that recurrence network measures, particularly transitivity, local clustering coefficient, assortativity, and betweenness centrality can successfully distinguish between deterministic chaotic and stochastic processes (after additional embedding) due to their sensitivity to the presence of UPOs. Our results also show that recurrence network measures like transitivity and average path length are robust against noise and perform better than the Complexity-Entropy plane method at short data lengths. Furthermore, our results show that the effect of noise on the recurrence network measures can be minimized by increasing the recurrence rate.For the analysis of real-world data such as EEG signals, we combined the recurrence network approach with surrogate data to test for the structural complexity in healthy and epileptic EEG signals. Here our results point to an increasing complexity of EEG recordings when moving from healthy to epileptic conditions. Furthermore, we used both univariate network measure and bivariate cross-network measure to distinguish between the structural properties of interictal EEG signals recorded from epileptic and nonepileptic brain areas. Here, our results clearly demonstrated that interictal EEG signals recorded from epileptic areas are more deterministic and interdependent compared to interictal activity recorded from nonepileptic areas. Finally, we show that recurrence network analysis can be applied to uncover the dynamical transitions in neural signals using short segments of data (≈ 150 to 500 samples). To demonstrate this, we used two kinds of neural data - epileptic EEG data and local field potential (LFP) signals recorded during a visuomotor task. We observed that the temporal fluctuations observed in the recurrence network measures are consistent with the dynamical transitions underlying the epileptic and task-based LFP signals.To conclude, recurrence network analysis analysis can capture the complexity in the organization of EEG data in different dynamical states in a more elaborated fashion compared to other approaches such as nonlinear prediction error or correlation dimension. By means of the recurrence network measures, this difference can be assessed not only qualitatively (as when using as tests for nonlinearity), but also quantitatively. Thus, coupled with its ability to operate on short-window sizes and robustness to noise, recurrence network analysis can be a powerful tool to analyze the dynamics of multi-scale neural signals

A future for intelligent autonomous ocean observing systems

Ocean scientists have dreamed of and recently started to realize an ocean observing revolution with autonomous observing platforms and sensors. Critical questions to be answered by such autonomous systems are where, when, and what to sample for optimal information, and how to optimally reach the sampling locations. Definitions, concepts, and progress towards answering these questions using quantitative predictions and fundamental principles are presented. Results in reachability and path planning, adaptive sampling, machine learning, and teaming machines with scientists are overviewed. The integrated use of differential equations and theory from varied disciplines is emphasized. The results provide an inference engine and knowledge base for expert autonomous observing systems. They are showcased using a set of recent at-sea campaigns and realistic simulations. Real-time experiments with identical autonomous underwater vehicles (AUVs) in the Buzzards Bay and Vineyard Sound region first show that our predicted time-optimal paths were faster than shortest distance paths. Deterministic and probabilistic reachability and path forecasts issued and validated for gliders and floats in the northern Arabian Sea are then presented. Novel Bayesian adaptive sampling for hypothesis testing and optimal learning are finally shown to forecast the observations most informative to estimate the accuracy of model formulations, the values of ecosystem parameters and dynamic fields, and the presence of Lagrangian Coherent Structures