The study of nonlinear systems and chaos is of great importance to science and engineering mainly because real systems are inherently nonlinear and linearization is only valid near the operating point. The interest in chaos was increased when Lorenz accidentally discovered the sensitivity to initial condition during his simulation work on weather prediction. When a nonlinear system is exhibiting

Fractional Order Systems: Optimization, Control, Circuit Realizations and Applications consists of 21 contributed chapters by subject experts. Chapters offer practical solutions and novel methods for recent research problems in the multidisciplinary applications of fractional order systems, such as FPGA, circuits, memristors, control algorithms, photovoltaic systems, robot manipulators

It is well-known that discovering and then calculating all branches of solutions of fractional order nonlinear differential equations with boundary conditions can be difficult even by numerical methods. To overcome this difficulty, in this chapter two semianalytic methods are presented to predict and obtain multiple solutions of nonlinear boundary value problems. These methods are based on the

Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from

This chapter introduces two FPGA implementations of the fractional-order operators: the Caputo and the Grünwald-Letnikov (GL) derivatives. First, the Caputo derivative is realized using nonuniform segmentation to reduce the size of the Look-Up Table. The Caputo implementation introduced can generate derivatives of previously defined functions only. Generic and complete hardware architecture of the

Area and power consumption are the main challenges in Network on Chip (NoC). Indeed, First Input First Output (FIFO) memory is the key element in NoC. Increasing the FIFO depth, produces an increas in the performance of NoC but at the cost of area and power consumption. This paper proposes a new hybrid CMOS-Memristor based FIFO architecture that consumes low power and has a small size compared to

This chapter introduces optimization algorithms for parameter extractions of three fractional-order circuits that model bioimpedance. The Cole-impedance model is investigated; it is considered one of the most commonly used models providing the best fit with the measured data. Two new models are introduced: the fractional Hayden model and the fractional-order double-shell model. Both models are the

Pulsed wave Doppler ultrasound is commonly used in the diagnosis of cardiovascular and blood flow abnormalities. Doppler techniques have gained clinical significance due to its safety, real-time performance and affordability. This work presents the development of a pulsed wave spectral Doppler module, which was integrated into a reconfigurable ultrasound system. The targeted system adopts a

Memristor has become an interesting research subject in the recent years. Its special behavior has attracted the attention of the research community that motivated researchers to investigate it in details. As memristor is a relatively new electrical element, it is not yet available in the market as a solid state component Researchers found their way to build memristor emulators to achieve its

Fractional-order models of supercapacitors are advantageous in that they have fewer terms, offering simpler expressions to accurately describe the transient characteristics of these devices than integer-order models. When evaluating the discharge characteristics of supercapacitors, a constant current is often considered which does necessarily represent real-world applications. In this work, the