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).

Behavioral changes in Rattus norvegicus experimentally infected by Toxocara canis larvae

Toxocara canis is a common canine nematode parasite and one of its possible transmission mechanisms is the predation of infected rodents by canids. Fifty Rattus norvegicus were used to study behavioral alterations in rodents infected by T. canis larvae. The rats were divided into three groups: G1, 20 rats infected with 300 T. canis eggs; G2, 20 rats infected with 2,000 T. canis eggs; and G3, 10 non-infected rats. Thirty and 60 days post-infection, rats from all the groups were submitted to an open-field apparatus for five min and subsequently, to an elevated plus-maze apparatus, again for five min. The data obtained indicated improvement in mobility (total locomotion time and rearing frequency) and exploratory behavior in infected rats, principally in G2, which provides some support for the hypothesis that behavioral alterations in rodents infected by Toxocara canis larvae enhance the transmission rate of this ascarid to dogs.

Behavioral changes in Rattus norvegicus coinfected by Toxocara canis and Toxoplasma gondii

Using an elevated plus maze apparatus and an activity cage, behavioral changes in Rattus norvegicus concomitantly infected by Toxocara canis and Toxoplasma gondii were studied, during a period of 120 days. Rats infected by Toxocara canis or Toxoplasma gondii showed significant behavioral changes; however, in the group coinfected by both parasites a behavioral pattern similar to that found in the group not infected was observed thirty days after infection, suggesting the occurrence of modulation in the behavioral response.

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.

BEHAVIORAL AND MEMORY CHANGES IN Mus musculus COINFECTED BY Toxocara canis AND Toxoplasma gondii

Several researchers have stated that parasites can alter the behavior of their hosts, in order to increase the transmission rate, principally when prey-predator relationships are a reliable way of infection transmission. The aim of this study was to verify the occurrence of changes in anxiety and short-term memory patterns in experimentally infected Mus musculus by Toxocara canis and/or Toxoplasma gondii. Forty male Mus musculus (Balb/c) eight-week-old were divided into four groups of 10 mice each. One group was infected with 300 eggs of Toxocara canis; a second group was submitted to infection with 10 cysts of Toxoplasma gondii; a third group was concomitantly infected with both parasites with the same inoculums and the last group was maintained without infection. The anxiety levels were evaluated using an elevated plus maze and an actometer; the short-term memory was determined by a two-way active avoidance equipment. The determination of anxiety levels were conducted 40 and 70 days after infection and the short-term memory was evaluated 140 days after infection. Mice chronically infected by Toxoplasma gondii showed impaired learning and short-term memory, but no significant differences were found in mice infected by Toxocara canis or concomitantly infected by Toxocara canis and Toxoplasma gondii when compared to non infected mice.

The Role of Sensory Modulation Deficits and Behavioral Symptoms in a Diagnosis for Early Childhood

To contribute to the validation of the sensory and behavioral criteria for Regulation Disorders of Sensory Processing (RDSP) (DC:0-3R, 2005), this study examined a sample of toddlers in a clinical setting to analyze: (1) the severity of sensory modulation deficits and the behavioral symptoms of RDSP; (2) the associations between sensory and behavioral symptoms; and (3) the specific role of sensory modulation deficits in an RDSP diagnosis. Based on clinical observations, 78 toddlers were classified into two groups: toddlers with RDSP (N = 18) and those with‘‘other diagnoses in Axis I/II of the DC:0-3R’’ (OD3R; N = 60). The parents completed the Infant Toddler Sensory Profile and the Achenbach Checklist. The results revealed that the RDSP group had more severe sensory modulation deficits and specific behavioral symptoms; stronger, although not significant, associations between most sensory and behavioral symptoms; and a significant sensory modulation deficit effect. These findings support the validity of RDSP.

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.