Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems

MSC 2010: 26A33, 34D05, 37C25In the paper, long-time behavior of solutions of autonomous two-component incommensurate fractional dynamical systems with derivatives in the Caputo sense is investigated. It is shown that both the characteristic times of the systems and the orders of fractional derivatives play an important role for the instability conditions and system dynamics. For these systems, stationary solutions can be unstable for wider range of parameters compared to ones in the systems with integer order derivatives. As an example, the incommensurate fractional FitzHugh-Nagumo model is considered. For this model, different kinds of limit cycles are obtained by the method of computer simulation. A common picture of non-linear dynamics in fractional dynamical systems with positive and negative feedbacks is presented

Engineering Education and Research Using MATLAB

MATLAB is a software package used primarily in the field of engineering for signal processing, numerical data analysis, modeling, programming, simulation, and computer graphic visualization. In the last few years, it has become widely accepted as an efficient tool, and, therefore, its use has significantly increased in scientific communities and academic institutions. This book consists of 20 chapters presenting research works using MATLAB tools. Chapters include techniques for programming and developing Graphical User Interfaces (GUIs), dynamic systems, electric machines, signal and image processing, power electronics, mixed signal circuits, genetic programming, digital watermarking, control systems, time-series regression modeling, and artificial neural networks

Spins in Thin Films and Nanodevices

The central theme of this work is the engineering of devices and materials that exhibit spin dependent phenomena. In particular, the spin orientation of charge carriers can play a central role in transport, especially in magnetic or other spin correlated media. Propagation of charge carriers with net spin results in a transfer of angular momentum that can excite static and dynamical states in active device elements. To utilize such phenomena in practical devices, new mew means of device characterization and optimization must be developed. To that end, we have performed experiments which elucidate some of the mechanisms underlying spin dependent transport phenomena.;We report the observation of hysteretic synchronization of point contact spin torque nano-oscillators (STNOs) by a microwave magnetic field. The hysteresis was asymmetric with respect to the frequency detuning of the driving signal, and appeared in the region of a strong dependence of the oscillation frequency on the bias current. Theoretical analysis showed that hysteretic synchronization occurred when the width of the synchronization range, enhanced by the oscillator\u27s nonlinearity, became comparable to the dissipation rate, while the observed asymmetry was a consequence of the nonlinear dependence of frequency on the bias current.;Another emergent phenomenon was a series of fractional synchronization regimes in a STNO driven by a microwave field. These regimes are characterized by rational relations between the driving frequency and the frequency of the oscillation. Analysis based on the phase model of auto-oscillator indicates that fractional synchronization becomes possible when the driving signal breaks the symmetry of the oscillation, while the synchronization ranges are determined by the geometry of the oscillation orbit. Measurements of fractional synchronization were utilized to obtain information about the oscillation characteristics in nanoscale systems not accessible to direct imaging techniques.;Oxidation in magnetic nanosystems can result in changes of the magnetic ordering of active layers in devices, resulting in degraded device performance. We demonstrate that magnetic multilayer nanopillars can be efficiently protected from oxidation by coating with silicon. Both the protected and the oxidized nanopillars exhibited an increase of reversal current at cryogenic temperatures. However the magnetic excitation onset current increased only in the oxidized samples. We show that oxidized nanopillars exhibit anomalous switching statistics at low temperature, providing a simple test for the quality of magnetic nanodevices.;We studied exchange bias in magnetic multilayers incorporating antiferromagnet CoO doped with up to 35 atomic percent of Pt. The exchange bias increased with doping in epitaxial films, but did not significantly change in polycrystalline films at the lowest measured temperature of 5 K, and decreased at higher temperatures. We explain our results by the increased granularity of the doped antiferromagnetic films, resulting in simultaneous enhancement of the uncompensated spin density and reduction of the magnetic stability of antiferromagnetic grains.;Finally, we demonstrate the growth of Bi2Se3, a material known as a topological insulator (TI). The structural and electronic properties of Bi2Se3 films grown on Al2O 3 (110) by molecular beam epitaxy were investigated. The epitaxial films grew in the Frank-van der Merwe mode and were c-axis oriented. They exhibited the highest crystallinity, the lowest carrier concentration, and optimal stoichiometry at a substrate temperature of 200 .C determined by the balance between surface kinetics and desorption of selenium. The crystallinity of the films improved with increasing selenium/bismuth flux ratio

The challenge of non-Markovian energy balance models in climate

We first review the way in which Hasselmann’s paradigm, introduced in 1976 and recently honored with the Nobel Prize, can, like many key innovations in complexity science, be understood on several different levels. It can be seen as a way to add variability into the pioneering energy balance models (EBMs) of Budyko and Sellers. On a more abstract level, however, it used the original stochastic mathematical model of Brownian motion to provide a conceptual superstructure to link slow climate variability to fast weather fluctuations, in a context broader than EBMs, and led Hasselmann to posit a need for negative feedback in climate modeling. Hasselmann’s paradigm has still much to offer us, but naturally, since the 1970s, a number of newer developments have built on his pioneering ideas. One important one has been the development of a rigorous mathematical hierarchy that embeds Hasselmann-type models in the more comprehensive Mori-Zwanzig generalized Langevin equation (GLE) framework. Another has been the interest in stochastic EBMs with a memory that has slower decay and, thus, longer range than the exponential form seen in his EBMs. In this paper, we argue that the Mori-Kubo overdamped GLE, as widely used in statistical mechanics, suggests the form of a relatively simple stochastic EBM with memory for the global temperature anomaly. We also explore how this EBM relates to Lovejoy et al.’s fractional energy balance equation

Fractional order models of the human respiratory system

The fractional calculus is a generalization of classical integer-order integration and derivation to fractional (non-integer) order operators. Fractional order (FO) models are those models which contain such fractional order operators. A common representation of these models is in frequency domain, due to its simplicity. The dynamical systems whose model can be approximated in a natural way using FO terms, exhibit specific features, such as viscoelasticity, diffusion and a fractal structure; hence the respiratory system is an ideal application for FO models. Although viscoelastic and diffusive properties were intensively investigated in the respiratory system, the fractal structure was ignored. Probably one of the reasons is that the respiratory system does not pose a perfect symmetry, hence failing to satisfy one of the conditions for being a typical fractal structure. In the 70s, the respiratory impedance determined by the ratio of air-pressure and air-flow, has been introduced in a model structure containing a FO term. It has also been shown that the fractional order models outperform integer-order models on input impedance measurements. However, there was a lack of underpinning theory to clarify the appearance of the fractional order in the FO model structure. The thesis describes a physiologically consistent approach to reach twofold objectives: 1. to provide a physiologically-based mathematical explanation for the necessity of fractional order models for the input impedance, and 2. to determine the capability of the best fractional order model to classify between healthy and pathological cases. Rather than dealing with a specific case study, the modelling approach presents a general method which can be used not only in the respiratory system application, but also in other similar systems (e.g. leaves, circulatory system, liver, intestines). Furthermore, we consider also the case when symmetry is not present (e.g. deformations in the thorax - kyphoscoliose) as well as various pathologies. We provide a proof-of-concept for the appearance of the FO model from the intrinsic structure of the respiratory tree. Several clinical studies are then conducted to validate the sensitivity and specificity of the FO model in healthy groups and in various pathological groups

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. [...

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio