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## Über dieses Buch

This book focuses on modelling and simulation, control and optimization, signal processing, and forecasting in selected nonlinear dynamical systems, presenting both literature reviews and novel concepts. It develops analytical or numerical approaches, which are simple to use, robust, stable, flexible and universally applicable to the analysis of complex nonlinear dynamical systems. As such it addresses key challenges are addressed, e.g. efficient handling of time-varying dynamics, efficient design, faster numerical computations, robustness, stability and convergence of algorithms. The book provides a series of contributions discussing either the design or analysis of complex systems in sciences and engineering, and the concepts developed involve nonlinear dynamics, synchronization, optimization, machine learning, and forecasting. Both theoretical and practical aspects of diverse areas are investigated, specifically neurocomputing, transportation engineering, theoretical electrical engineering, signal processing, communications engineering, and computational intelligence. It is a valuable resource for students and researchers interested in nonlinear dynamics and synchronization with applications in selected areas.

## Inhaltsverzeichnis

### On the Construction of Dissipative Polynomial Nambu Systems with Limit Cycles

Abstract
In this chapter we study nonlinear Nambu systems with canonical dissipation in four dimensions in which prescribed limit cycles arise. For this purpose we discuss some possibilities to apply concepts from the geometry of four-dimensional Euclidean spaces in order to construct a desired intersection by a set of planes and surfaces. Since scalar Nambu functions are needed for the construction of Nambu systems, the relationship between these functions and hypersurfaces will be discussed. We illustrate our considerations by means of two examples of canonical dissipative (CD) Nambu systems in which limit cycles occur. Whereas we considered the synthesis problem of limit cycle circuits with the CD Nambu approach previously, we introduce in this paper an analysis concept based on CD Nambu systems for calculating nonisolated zeros of nonlinear equations.
Richard Mathis, Wolfgang Mathis

### On the Dynamics of Chaotic Systems with Multiple Attractors: A Case Study

Abstract
In this chapter, the dynamics of chaotic systems with multiple coexisting attractors is addressed using the well-known Newton–Leipnik system as prototype. In the parameters space, regions of multistability (where the system exhibits up to four disconnected attractors) are depicted by performing forward and backward bifurcation analysis of the model. Basins of attraction of various coexisting attractors are computed, showing complex basin boundaries. Owing to the fractal structure of basin boundaries, jumps between coexisting attractors are predicted in experiment. A suitable electrical circuit (i.e., analog simulator) is designed and used for the investigations. Results of theoretical analysis are verified by laboratory experimental measurements. In particular, the hysteretic behavior of the model is observed in experiment by monitoring a single control resistor. The approach followed in this chapter shows that by combining both numerical and experimental techniques, one can gain deep insight into the dynamics of chaotic systems exhibiting multiple attractor behavior.
J. Kengne, A. Nguomkam Negou, D. Tchiotsop, V. Kamdoum Tamba, G. H. Kom

### Multivaluedness Aspects in Self-Organization, Complexity and Computations Investigations by Strong Anticipation

Abstract
Since the introduction of strong anticipation by D. Dubois, numerous investigations of concrete systems have been proposed. In this chapter, new examples of discrete dynamical systems with anticipation are considered. The mathematical formulation of problems, possible analytical formulas for solutions, and numerical examples of possible solutions are proposed. One of the most interesting properties in such systems is the possible multivaluedness of the solutions. This can be considered from the point of view of dynamical chaos and complex behavior. We present examples of periodic and complex solutions, properties of attractors, and possible applications in self-organization. The main peculiarity is the strong anticipation property. General new possibilities include the possible multivaluedness of the dynamics of automata. Possible interpretations of such behavior of cellular automata are discussed. Further prospects for development of automata theory and hypercomputation are proposed.
Alexander Makarenko

### Nonlinear Modeling of Continuous-Wave Spin Detection Using Oscillator-Based ESR-on-a-Chip Sensors

Abstract
In this chapter, an advanced nonlinear energy-based modeling of LC tank oscillators used as sensors for ensembles of electron or nuclear spins is presented. Recently, this oscillator-based sensing principle has been gaining significant attention in the electron spin resonance community for biomedical and material science applications. Since the sensing principle relies on the coupling between a harmonic oscillator (the spin ensemble) and an intrinsically nonlinear electrical oscillator, it presents an excellent example of the high relevance of nonlinear dynamical systems modeling for practical sensing applications. In order to provide a self-contained overview, after a short general motivation that highlights the relevance of the topic, the chapter begins with a description of the experimental setup of the oscillator-based spin-detection approach, which is somewhat different from that for conventional resonator-based detection. In this description, it is shown how continuous-wave spin-detection experiments can be carried out using LC tank oscillators by monitoring the oscillation frequency when sweeping the static magnetic field $$B_0$$. At this point, it is also explained how standard field modulation using a modulation field $$B_\mathrm {m}$$ parallel to $$B_0$$ can be used to increase the signal-to-noise ratio by means of phase-sensitive detection using a conventional lock-in amplifier. Then the interaction between the nonlinear electrical oscillator and the spin ensemble is modeled using the solution of the Bloch equation in the steady state, which models the dynamics of the spin ensemble, and the magnetic energy associated with the inductor of the LC tank oscillator. In this way, under steady-state conditions as they occur in continuous-wave ESR and NMR experiments, expressions for spin-related changes in inductance and resistance can be derived, which are in turn related to changes in the oscillation frequency and amplitude of the LC tank oscillator. To quantify the resulting change in oscillation frequency and also derive expressions for the expected noise floor, which eventually determines the achievable limit of detection, the chapter then provides a detailed discussion of the nonlinear modeling of LC tank oscillators in the presence of noise. The resulting model of the LC tank oscillator is subsequently used to find analytical expressions for the limit of detection of frequency-sensitive oscillator-based spin detectors. Finally, experimental results from a prototype realization of an oscillator-based CMOS ESR-on-a-chip detector are used to validate the accuracy of the derived signal and noise models.
Jens Anders

### Effect of Nonlinearity and Boiler Dynamics in Automatic Generation Control of Multi-area Thermal Power System with Proportional-Integral-Derivative and Ant Colony Optimization Technique

Abstract
This work presents the automatic generation control (AGC) of a multiarea interconnected power system. The investigated multiarea power system is prepared with three equal reheat thermal power systems with suitable governor unit, turbine unit, generator unit, speed regulator unit, tie-line in each unit, and secondary proportional-integral-derivative (PID) controller. During nominal loading conditions, the power generating unit offers good quality of power to consumers. Nevertheless, the occurrence of sudden load disturbance in the interconnected power generating unit affects the entire performance (consistency in system frequency and voltage) and system stability. In order to moderate this big pose, the PID controller is introduced as a secondary controller. Jointly with the proper selection of the controller parameters (proportional gain (KP), integral gain (KI), and derivative gain (KD)) a good quality of power supply is crucial in a power system for generating. An artificial intelligence (AI) based ant colony optimization (ACO) technique is considered for tuning the control parameters. Further, in the current chapter, nonlinearity and boiler dynamics effects are considered to evaluate the performance of the investigated power system. The nonlinearities are generation rate constraints (GRC) and governor dead band (GDB). The drum-type oil-fired boiler system is considered in this work. The nonlinearity effect and boiler dynamics in the investigated power systems are derived by considering different scenarios: (a) GRC in all areas and two percent step load perturbation (2% SLP) in area 1, (b) GDB in all areas and two percent step load perturbation (2% SLP) in area 1 (c) GRC and GDB in all areas and two percent step load perturbation (2% SLP) in area 1 and (d) GRC, GDB, and boiler dynamics (BD) in all areas and two-percent step load perturbation (2% SLP) in area 1. Time-domain specification analysis is used for the evaluation of nonlinearity and boiler dynamics effect.
K. Jagatheesan, B. Anand, K. Baskaran, N. Dey, A.S. Ashour, V.E. Balas

### A Review of Traffic Light Control Systems and Introduction of a Control Concept Based on Coupled Nonlinear Oscillators

Abstract
This chapter provides an in-depth overview of the state of the art on traffic light control and optimization. Several classical control systems, methods, concepts, tools, and strategies are described, and their related pros and cons are discussed. Four different types of control strategies are considered, pretimed, actuated, adaptive, and self-organized, and it is demonstrated that some strategies can be appropriate for local control, area control, or both (local and area). Further, the chapter develops a system of coupled nonlinear oscillators, that is used for traffic light control and optimization both at isolated junctions (i.e., local control) and in a network of coupled traffic junctions (i.e., area control). The case of an isolated traffic junction is modeled by coupled oscillators, each of which represents a specific phase group of the traffic light at the junction. The case of a network of coupled traffic junctions is also considered, and we show the possibility of modeling the traffic light at each junction by a single oscillator. The system developed is viewed as a modified version of the self-organized Kuramoto model for traffic light control due to some important features that are common to both systems (i.e., Kuramoto model and the system developed). The main advantage of the system developed is the possibility of dynamically monitoring the signals’ phases (delays), signal-splits, or signal timings according to the dynamic variation of the traffic demand in all conflicting approaches of the traffic junctions under investigation. The system of coupled nonlinear oscillators is considered a flexible platform, which is appropriate for modeling the four types of traffic light control strategies. Another advantage of the system developed is the possibility of an easy hardware implementation using electronic devices. This allows a straightforward possibility for designing appropriate electronic prototypes of traffic light controllers (appropriate for both local and area controls).
Jean Chamberlain Chedjou, Kyandoghere Kyamakya

### Neural-Network-Based Calibration of Macroscopic Traffic Flow Models

Abstract
This chapter proposes a neural-network-based calibration of macroscopic traffic flow models expressed in the form of nonlinear partial differential equations (PDEs). The calibration scheme/module developed aims at improving both accuracy and stability of the nonlinear PDE models in order to make them more realistic. In essence, the macroscopic nonlinear PDE models of traffic flow (proposed in the literature) are generally inaccurate, unstable, and unlikely to describe the realistic dynamics of traffic flow. To overcome these drawbacks we exploit the artificial neural network paradigm to build a concept called NN-PDE (neural network $$+$$ PDE solver), which involves the macroscopic model (in the form of a nonlinear partial differential equation) on the one hand, and the calibration scheme/module-based artificial neural network (ANN) on the other. The calibration scheme/module is used to dynamically adjust/optimize all outputs of the nonlinear “PDE” model in order to obtain a realistic set of parameters that could be used by the PDE model to describe the real/realistic dynamics of traffic flow. Overall, specific attention is devoted to some relevant issues related to the modeling concept such as accuracy, stability, and overfitting, just to name a few. These issues generally occur due to the complexity of the PDE model at stake for the sake of an accurate traffic flow model. Finally, some simulation results are shown to demonstrate the effectiveness of the NN-PDE concept developed.
Nkiediel Alain Akwir, Jean Chamberlain Chedjou, Kyandoghere Kyamakya

### Travelers in the Second Modernity: Where Technological and Social Dynamic Complexity Meet Each Other

Abstract
Can we speak of a totally normal chaos (Lash, Individualization in a Non-Linear Mode, 2002, [21]) of mobility in the second age of modernity? The current essay draws its inspiration mainly from the findings of systems theory and sociology about nonlinearity and individualization with particular application to mobility systems. Its first part analyzes the societal system of the second modernity as an open system with high nonlinearity. The second part applies reflections from the construction of hypotheses about the usage dynamics of an intelligent concept of social interaction on the move.
Oana Mitrea

### COMPRAM Assessment and System Dynamics Modeling and Simulation of Car-Following Model for Degraded Roads

Abstract
A.K. Kayisu, M.K. Joseph, K. Kyamakya

### Design of a Chaotic Pulse-Position Modulation Circuit

Abstract
An analog chaotic modulation circuit based on Chua’s circuit is proposed to generate a chaotic pulse-position signal. The circuit is designed with standard electronic components, and the parameters of the generated signals, including the pulse period, the modulation range of the pulse-position, even the probability distribution of the pulse-position, can be adjusted flexibly.
Junying Niu, Zhong Li, Yuhong Song, Wolfgang A. Halang

### Chaos-Based Digital Communication Systems with Low Data-Rate Wireless Applications

Abstract
This chapter presents a study on the modeling and performance evaluation of chaos-based coherent and incoherent systems, i.e., chaotic direct-sequence code-division multiple-access (CDS-CDMA) and differential chaos-shift keying (DCSK), for low-data-rate applications in wireless communications. This study is motivated by the design of a secure physical layer for wireless-based applications with low data rate and in small transmission areas. A wireless channel affected by noise, fading, multipath, and delay-spread for low-data-rate transmission of chaotically spreading signals is described and mathematically modeled. Discrete-time models for the transmitter and receiver of CDS-CDMA and DCSK systems under the impact of the wireless channel are developed. Bit error rate (BER) performance of the systems is estimated by means of both theoretical derivation and discrete integration. Simulated performances are shown and compared with the corresponding estimated ones, where the effects of the ratio $$E_b/N_0$$, spreading factor, number of users, sample rate, and the number of transmission paths on the BER are fully evaluated. The obtained results showed that the low-rate chaos-based systems can exploit the multipath nature of wireless channels in order to improve their BER performances. This feature indicates that chaos-based communication systems are a promising and robust solution for enhancing physical layer security in low-rate wireless personal area networks (LR-WPANs).
Nguyen Xuan Quyen, Kyandoghere Kyamakya

### Nonlinear Programming Approach for Design of High Performance Sigma–Delta Modulators

Abstract
In this chapter we present a nonlinear programming approach to the design of third-order sigma–delta modulators with respect to maximization of the signal-to-noise ratio, taking into account the modulator’s stability. The proposed approach uses an analytic formula for calculation of the signal-to-noise ratio and an analytic formula for stability of the modulator. Thus the goal function becomes maximization of the signal-to-noise ratio and constraints come from stability issues and bounds of the modulator noise transfer function coefficients. The results are compared with the optimal third-order modulator design provided by DStoolbox. The proposed procedure has low computation requirements. It is described for third-order modulators with one real pole of the loop filter transfer function and can be extended easily and generalized to higher-order modulators.

### Emotion Recognition Involving Physiological and Speech Signals: A Comprehensive Review

Abstract
Emotions play an extremely important role in how we make decisions, in planning, in reasoning, and in other human mental states. The recognition of a driver’s emotions is becoming a vital task for advanced driver assistance systems (ADAS). Monitoring drivers’ emotions while driving offers drivers important feedback that can be useful in preventing accidents. The importance comes from the fact that driving in aggressive moods on road leads to traffic accidents. Emotion recognition can be achieved by analyzing facial expression, speech, and various other biosignals such as electroencephalograph (EEG), blood volume pulse (BVP), electrodermal skin resistance (EDA), electrocardiogram (ECG), etc. In this chapter, a comprehensive review of the state of-the-art methodologies for emotion recognition based on physiological changes and speech is presented. In particular, we investigate the potential of physiological signals and driver’s speech for emotion recognition and their requirements for ADAS. All steps of an automatic recognition system are explained: emotion elicitation, data preprocessing such as noise and artifacts removal, features extraction and selection, and finally classification.

### A Hybrid Reasoning Approach for Activity Recognition Based on Answer Set Programming and Dempster–Shafer Theory

Abstract
This chapter discusses a promising approach for multisensor-based activity recognition in smart homes. The research originated in the domain of active and assisted living, particularly in the field of supporting people in mastering their daily life activities. The chapter proposes (a) a reasoning method based on answer set programming that uses different types of features for selecting the optimal sensor set, and (b) a fusion approach to combine the beliefs of the selected sensors using an advanced evidence combination rule of Dempster–Shafer theory. In order to check the overall performance, this approach was tested with the HBMS dataset on an embedded platform. The results demonstrated a highly promising accuracy compared to other approaches.
Fadi Al Machot, Heinrich C. Mayr, Suneth Ranasinghe

### Estimation of Infection Force of Hepatitis C Virus Among Drug Users in France

Abstract
The spread of diseases is a dynamic and complex phenomenon. In the world, they are due to misery and poverty. To understand epidemiological systems is essential for governments. Since modeling simplifies reality, it is an excellent method. The hepatitis C virus (HCV) infection is common worldwide, and injection drug use remains the major mode of transmission of the disease, especially because of equipment sharing. Consequently, it is crucial to monitor the HCV transmission dynamics over time and to assess the effect of harm reduction measures. The aim of this work is to estimate the force of infection of hepatitis C from two national cross-sectional epidemiological surveys conducted in 2004 and 2011 by the French Institute for Public Health Surveillance and its partners in a drug user population in France. HCV prevalence was estimated according to age and calendar time through fractional polynomials adjusted or not to the HIV serological status and to injected drug users or oral drug users in general. The force of infection was modeled according to an SIS (susceptible–infected–susceptible) compartmental model using ordinary differential equations (ODE) and as a function of the derivative of the prevalence function depending on age, time, HIV serological status, and having injected at least once in their life, from 2000 to 2020. Our model was applied on real and simulated surveys using R and Stata software. The results show that HCV prevalence and the force of infection are linked to age and time, and are very high for drug users who injected at least once in their life and who are simultaneously HCV and HIV infected. Based on this model, we estimated that HCV incidence will continue to decline over the following years. Currently in France, there is no cohort study of the HCV among drug users. The only way to estimate HCV incidence in the French population is to use the only existing two national cross-sectional surveys. Our work provides guidance for researchers to compare several cross-sectional epidemiological surveys among drug users and proposes an alternative method to estimate the force of infection among drug users from cross-sectional surveys in the absence of a cohort.
Selain Kasereka, Yann Le Strat, Lucie Léon

### Neurocomputing-Based Matrix Inversion: A Critical Review of the Related State of the Art

Abstract
Solving matrix inversion is very useful in many areas of science (e.g., in physics and engineering, such as chemical processes, robotics, electronic circuits, engineered materials, and other natural sciences). Various methods exist to solve matrix inversion problems. Most of them are very good algorithms, which, however, have the drawback of being efficient only when implemented on single-processor systems. Therefore, those algorithms are very inefficient when implemented on multiprocessor platforms; thus, they lack sufficient parallelizability. The main root of the problem lies in the nature of the algorithms, since they were originally designed for implementations on single-processor systems. Some novel concepts involving neurocomputing, however, have the potential for more efficiency in multicore environments. This chapter provides a comprehensive overview of both traditional and neurocomputing-based methods for solving the matrix inversion problem (i.e., analytical, heuristics, dynamical-system-based methods, etc.). These methods are compared based on some important criteria including convergence, parallelizability/scalability, accuracy, and applicability to time-varying matrices. Finally, we propose a new concept based on neurocomputing for solving the matrix inversion problem. The main advantage of this concept is the possibility of efficiently satisfying all the important criteria.
Vahid Tavakkoli, Jean Chamberlain Chedjou, Kyandoghere Kyamakya
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