Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

An efficient compression of ECG signals using deep convolutional autoencoders

Synchronization Systems in Communication and Control

Chaos control means to design a controller that is able to mitigating or eliminating the chaos behavior of nonlinear systems that experiencing such phenomenon. In this paper, a nonlinear Sliding-Mode Controller (SMC) is presented. Two nonlinear chaotic systems are chosen to be our case study in this paper, the well known Chua’s circuit and Lorenz system. The study shows the effectiveness of the designed nonlinear Sliding-Mode Controller.

Chaos control using sliding-mode theory

The expected widespread usage of Internet-of-Things (IoT) devices and the associated diversity of applications will place extra pressure on network resources including bandwidth availability. In networking within IoT, spectrum scarcity requires the consideration of the adaptive cognitive radio (CR) technology to achieve interference-free and on-demand IoT solutions for a number of applications. However, CR networks share the same security weaknesses of legacy wireless networks. Jamming is considered a common attack, where jammers can attack networks in a proactive or reactive approach. In this paper, we study the channel assignment problem under both proactive and reactive jamming attacks. Specifically, we propose a novel probabilistic-based channel assignment mechanism that aims at minimizing the invalidity ratio of CR packet transmissions subject to delay constraints. The proposed scheme exploits the statistical information of licensed primary users activities, fading conditions and jamming attacks over idle channels to provide communicating CR IoT devices with the most secured channels of lowest invalidity ratios. Simulation results show that our proposed security, availability, and quality-aware channel assignment algorithm can significantly improve network performance.

Spectrum Assignment in Cognitive Radio Networks for Internet-of-Things Delay-Sensitive Applications Under Jamming Attacks

Previous study showed that a third-order phase-locked loop (PLL) with sinusoidal phase detector characteristics experienced a Hopf bifurcation point as well as chaotic behavior. As a result, this behavior drives the PLL to the out-of-lock (unstable) state. The analysis was based on a modern nonlinear theory such as bifurcation and chaos. The main goal of this paper is to control this chaotic behavior. A nonlinear controller based on the theory of backstepping is designed. The study showed the effectiveness of the designed nonlinear controller in controlling the undesirable unstable behavior and pulling the PLL back to the in-lock state.

Chaos control of third-order phase-locked loops using backstepping nonlinear controller

The chaos induced in a new type of phase locked loop (PLL) having a second-order loop filter is investigated. The system under consideration is modeled as a third-order autonomous system with sinusoidal phase detector characteristics. The modern of nonlinear theory such as bifurcation and chaos is applied to a third-order of PLL. A method is developed to quantitatively study the type of bifurcations that occur in this type of PLL’s. The study showed that PLL experiencing a Hopf bifurcation point as well as chaotic behaviour. The method of multiple scales is used to find the normal form near the Hopf bifurcation point. The point is found to be supercritical one.

Chaos and bifurcation in a third-order phase locked loop

In this paper, a nonlinear backstepping controller has been designed to control bifurcation as well as incipient chaos that has been experienced in the RCLSJ (shunted nonlinear resistive-capacitive-inductance) Josephson-Junction. The results show that the system, without controller, has a dangerous Hopf bifurcation point that lead to chaotic behavior. For certain values of the external direct current (I0), the system becomes chaotic. On the other hand, the nonlinear backstepping controller converts the chaotic region into a stable periodic solution region

Controlling Chaos in Josephson-Junction Using Nonlinear Backstepping Controller

The adjacent channel interference (ACI) resulting from imperfect filtering can severely degrade the performance of any wireless communication system. Despite this fact, most of previously proposed medium access control (MAC) protocols for cognitive radio networks (CRNs) were designed while ignoring the effects of ACI (assuming ideal filtering). The effect of ACI can be reduced by introducing guard bands (GBs). However, this solution comes at the expense of degrading spectrum efficiency. In this paper, we develop an efficient GB-aware MAC protocol that attempts at maximizing network throughput while improving fairness in CRNs. Unlike most of previously proposed GB-aware MAC protocols that perform channel assignment sequentially, our MAC performs the channel assignment for multiple CR links simultaneously (the so-called batch method). Batching enables concurrent channel assignment for multiple CR links, which consequently allows for concurrent data transmissions. Batching can be realized by introducing an admission control phase for CR users to share their control information. The batch method can effectively provide distributed decisions that achieve better throughput while reducing the number of GBs. Our MAC also allows the CR users to utilize the reserved GBs of primary networks under predefined FCC power constraints. Simulation results indicate that our protocol achieves significant performance improvement compared to previous GB-aware protocols.

A Batch-Based MAC Design With Simultaneous Assignment Decisions for Improved Throughput in Guard-Band-Constrained Cognitive Networks

A new hybrid two-stage electrocardiogram (ECG) signal compression method based on the modified discrete cosine transform (MDCT) and discrete wavelet transform (DWT) is proposed. The ECG signal is partitioned into blocks and the MDCT is applied to each block to decorrelate the spectral information. Then, the DWT is applied to the resulting MDCT coefficients. Removing spectral redundancy is achieved by compressing the subordinate components more than the dominant components. The resulting wavelet coefficients are then thresholded and compressed using energy packing and binary-significant map coding technique for storage space saving. Experiments on ECG records from the MIT-BIH database are performed with various combinations of MDCT and wavelet filters at different transformation levels, and quantization intervals. The decompressed signals are evaluated using percentage rms error (PRD) and zero-mean rms error (PRD(1)) measures. The results showed that the proposed method provides low bit-rate and high quality of the reconstructed signal. It offers average compression ratio (CR) of 21.5 and PRD of 5.89%, which would be suitable for most monitoring and diagnoses applications. Simulation results show that the proposed method compares favourably with various state-of-the-art ECG compressors.

http://www.aun.edu.eg/journal_files/186_J_2606.pdf

Bassam Harb

Papers

Chaos control of third-order phase-locked loops using backstepping nonlinear controller

Chaos and bifurcation in a third-order phase locked loop

Controlling Chaos in Josephson-Junction Using Nonlinear Backstepping Controller

A Batch-Based MAC Design With Simultaneous Assignment Decisions for Improved Throughput in Guard-Band-Constrained Cognitive Networks

ECG signal compression using combined modified discrete cosine and discrete wavelet transforms.