Fractional Dynamics Representation in the Pseudo Phase Plane

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

Control and Dynamics of Fractional Order Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades due to the progress in the area of nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion.

Fractional Dynamics and Control of Distributed Parameter Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of some distributed parameter systems.

Chaos Dynamics in the Trajectory Conjtrol of Redundant Manipulators

Nonlinear Dynamics, chaos, Control, and Their Applications to Engineering Sciences: Vol. 6 - Applications of nonlinear phenomena

Fractional Dynamics in Forest Fires

Every year forest fires consume large areas, being a major concern in many countries like Australia, United States and Mediterranean Basin European Countries (e.g., Portugal, Spain, Italy and Greece). Understanding patterns of such events, in terms of size and spatiotemporal distributions, may help to take measures beforehand in view of possible hazards and decide strategies of fire prevention, detection and suppression. Traditional statistical tools have been used to study forest fires. Nevertheless, those tools might not be able to capture the main features of fires complex dynamics and to model fire behaviour [1]. Forest fires size-frequency distributions unveil long range correlations and long memory characteristics, which are typical of fractional order systems [2]. Those complex correlations are characterized by self-similarity and absence of characteristic length-scale, meaning that forest fires exhibit power-law (PL) behaviour. Forest fires have also been proved to exhibit time-clustering phenomena, with timescales of the order of few days [3]. In this paper, we study forest fires in the perspective of dynamical systems and fractional calculus (FC). Public domain forest fires catalogues, containing data of events occurred in Portugal, in the period 1980 up to 2011, are considered. The data is analysed in an annual basis, modelling the occurrences as sequences of Dirac impulses. The frequency spectra of such signals are determined using Fourier transforms, and approximated through PL trendlines. The PL parameters are then used to unveil the fractional-order dynamics characteristics of the data. To complement the analysis, correlation indices are used to compare and find possible relationships among the data. It is shown that the used approach can be useful to expose hidden patterns not captured by traditional tools.

Symmetry and order parameter dynamics of the human odometer

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary bipedal gaits (e.g., walk, run) are characterized by dihedral symmetry, whereas secondary bipedal gaits (e.g., gallop-walk, gallop- run) are characterized by a lower, cyclic symmetry. This fact has been used in tests of human odometry (e.g., Turvey et al. in P Roy Soc Lond B Biol 276:4309–4314, 2009, J Exp Psychol Hum Percept Perform 38:1014–1025, 2012). Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. The present research (a) extends these findings from overground locomotion to treadmill locomotion and (b) assesses a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of those dynamics. The results suggest that the symmetries and dynamics of distance measurement by the human odometer are the same whether the odometer is in motion relative to a stationary ground or stationary relative to a moving ground.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Simulation of masonry out-of-plane failure modes by multi-body dynamics

The seismic assessment of the local failure modes in existing masonry buildings is currently based on the identification of the so-called local mechanisms, often associated with the out-of-plane wall behavior, whose stability is evaluated by static force-based approaches and, more recently, by some displacement-based proposals. Local mechanisms consist of kinematic chains of masonry portions, often regarded as rigid bodies, with geometric nonlinearity and concentrated nonlinearity in predefined contact regions (unilateral no-tension behavior, possible sliding with friction). In this work, the dynamic behavior of local mechanisms is simulated through multi-body dynamics, to obtain the nonlinear response with efficient time history analyses that directly take into account the characteristics of the ground motion. The amplification/filtering effects of the structure are considered within the input motion. The proposed approach is validated with experimental results of two full-scale shaking-table tests on stone masonry buildings: a sacco-stone masonry façade tested at Laboratório Nacional de Engenharia Civil and a two-storey double-leaf masonry building tested at European Centre for Training and Research in Earthquake Engineering (EUCENTRE).

Land cover dynamics in Savanna Ecosystem of Borena Ethiopia

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Urban land cover change detection analysis and modeling spatio-temporal Growth dynamics using Remote Sensing and GIS Techniques: A case study of Dhaka, Bangladesh

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Analysis of the EEG Dynamics of Epileptic Activity in Gelastic Seizures Using Decomposition in Independent Components

Objective: Gelastic seizures are a frequent and well established manifestation of the epilepsy associated with hypothalamic hamartomas. The scalp EEG recordings very seldom demonstrate clear spike activity and the information about the ictal epilepsy dynamics is limited. In this work, we try to isolate epileptic rhythms in gelastic seizures and study their generators. Methods: We extracted rhythmic activity from EEG scalp recordings of gelastic seizures using decomposition in independent components (ICA) in three patients, two with hypothalamic hamartomas and one with no hypothalamic lesion. Time analysis of these rhythms and inverse source analysis was done to recover their foci of origin and temporal dynamics. Results: In the two patients with hypothalamic hamartomas consistent ictal delta (2–3 Hz) rhythms were present, with subcortical generators in both and a superficial one in a single patient. The latter pattern was observed in the patient with no hypothalamic hamartoma visible in MRI. The deep generators activated earlier than the superficial ones, suggesting a consistent sub-cortical origin of the rhythmical activity. Conclusions: Our data is compatible with early and brief epileptic generators in deep sub-cortical regions and more superficial ones activating later. Significance: Gelastic seizures express rhythms on scalp EEG compatible with epileptic activity originating in sub-cortical generators and secondarily involving cortical ones.

Analysis of the Dynamics and Origin of Epileptic Activity in Patients with Tuberous Sclerosis Evaluated for Surgery of Epilepsy

Objective: The epilepsies associated with the tuberous sclerosis complex (TSC) are very often refractory to medical therapy. Surgery for epilepsy is an effective alternative when the critical link between the localization of seizure onset in the scalp and a particular cortical tuber can be established. In this study we perform analysis of ictal and interictal EEG to improve such link. Methods: The ictal and interictal recordings of four patients with TSC undergoing surgery for epilepsy were submitted to independent component analysis (ICA), followed by source analysis, using the sLORETA algorithm. The localizations obtained for the ictal EEG and for the average interictal spikes were compared. Results: The ICA of ictal EEG produced consistent results in different events, and there was good agreement with the tubers that were successfully removed in three of the four patients (one patient refused surgery). In some patients there was a large discrepancy between the localization of ictal and interictal sources. The interictal activity produced more widespread source localizations. Conclusions: The use of ICA of ictal EEG followed by the use of source analysis methods in four cases of epilepsy and TSC was able to localize the epileptic generators very near the lesions successfully removed in surgery for epilepsy. Significance: The ICA of ictal EEG events may be a useful add-on to the tools used to establish the connection between epileptic scalp activity and the cortical tubers originating it, in patients with TSC considered for surgery of epilepsy.

Evolution of the Human Immunodeficiency Virus Type 2 Envelope in the First Years of Infection is Associated with the Dynamics of the Neutralizing Antibody Response

Background: Differently from HIV-1, HIV-2 disease progression usually takes decades without antiretroviral therapy and the majority of HIV-2 infected individuals survive as elite controllers with normal CD4+ T cell counts and low or undetectable plasma viral load. Neutralizing antibodies (Nabs) are thought to play a central role in HIV-2 evolution and pathogenesis. However, the dynamic of the Nab response and resulting HIV-2 escape during acute infection and their impact in HIV-2 evolution and disease progression remain largely unknown. Our objective was to characterize the Nab response and the molecular and phenotypic evolution of HIV-2 in association with Nab escape in the first years of infection in two children infected at birth. Results: CD4+ T cells decreased from about 50% to below 30% in both children in the first five years of infection and the infecting R5 viruses were replaced by X4 viruses within the same period. With antiretroviral therapy, viral load in child 1 decreased to undetectable levels and CD4+ T cells recovered to normal levels, which have been sustained at least until the age of 12. In contrast, viral load increased in child 2 and she progressed to AIDS and death at age 9. Beginning in the first year of life, child 1 raised high titers of antibodies that neutralized primary R5 isolates more effectively than X4 isolates, both autologous and heterologous. Child 2 raised a weak X4-specific Nab response that decreased sharply as disease progressed. Rate of evolution, nucleotide and amino acid diversity, and positive selection, were significantly higher in the envelope of child 1 compared to child 2. Rates of R5-to-X4 tropism switch, of V1 and V3 sequence diversification, and of convergence of V3 to a β-hairpin structure were related with rate of escape from the neutralizing antibodies. Conclusion: Our data suggests that the molecular and phenotypic evolution of the human immunodeficiency virus type 2 envelope are related with the dynamics of the neutralizing antibody response providing further support for a model in which Nabs play an important role in HIV-2 pathogenesis.

The Role of Prostaglandins in the Lower Urinary Tract Dynamics of Prostatectomized Patients: a Trial with Indomethacin and Aspirin

Using 49 prostatectomized patients as experimental subjects, we studied the effects of Inclometnacin and acetylsalicylic acid — accredited prostaglandin synthetase inhibitors — from a urodynamic and clinical standpoint. Relevant urodynamic data was gathered 1 hr 30 mi after the patients had taken the drugs and placebo. Clinical results were further scrutinized after 8 days of treatment, at which time a new urodynamic workup was again performed on some patients. Results were again studied shortly after the end of treatment. The effect of the drugs on bladder and urethral structures was borne out by clear-ct!t clinical and urodynamic changes. After statistically analyzing such changes, we concluded that prostaglandin synthesis inhibition resulting in the inhibition of prostaglandin action had, at least in part, led to the changes noted. In the present report we shall discuss the role played by the highly complex mechanisms at work.

Potencial Utilização de um Enterprise Resource Planning System para Suportar Práticas de Gestão de Conhecimento nas Organizações. Uma Aplicação com Dynamics Nav da Microsoft

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação