Fractional Dynamics of Computer Virus Propagation

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

New findings on the dynamics of HIV and TB coinfection models

In this paper we study a model for HIV and TB coinfection. We consider the integer order and the fractional order versions of the model. Let α∈[0.78,1.0] be the order of the fractional derivative, then the integer order model is obtained for α=1.0. The model includes vertical transmission for HIV and treatment for both diseases. We compute the reproduction number of the integer order model and HIV and TB submodels, and the stability of the disease free equilibrium. We sketch the bifurcation diagrams of the integer order model, for variation of the average number of sexual partners per person and per unit time, and the tuberculosis transmission rate. We analyze numerical results of the fractional order model for different values of α, including α=1. The results show distinct types of transients, for variation of α. Moreover, we speculate, from observation of the numerical results, that the order of the fractional derivative may behave as a bifurcation parameter for the model. We conclude that the dynamics of the integer and the fractional order versions of the model are very rich and that together these versions may provide a better understanding of the dynamics of HIV and TB coinfection.

Nonlinear dynamics of the patient’s response to drug effect during general anesthesia

In today’s healthcare paradigm, optimal sedation during anesthesia plays an important role both in patient welfare and in the socio-economic context. For the closed-loop control of general anesthesia, two drugs have proven to have stable, rapid onset times: propofol and remifentanil. These drugs are related to their effect in the bispectral index, a measure of EEG signal. In this paper wavelet time–frequency analysis is used to extract useful information from the clinical signals, since they are time-varying and mark important changes in patient’s response to drug dose. Model based predictive control algorithms are employed to regulate the depth of sedation by manipulating these two drugs. The results of identification from real data and the simulation of the closed loop control performance suggest that the proposed approach can bring an improvement of 9% in overall robustness and may be suitable for clinical practice.

Nonlinear dynamics of the patient’s response to drug effect during general anesthesia

In today’s healthcare paradigm, optimal sedation during anesthesia plays an important role both in patient welfare and in the socio-economic context. For the closed-loop control of general anesthesia, two drugs have proven to have stable, rapid onset times: propofol and remifentanil. These drugs are related to their effect in the bispectral index, a measure of EEG signal. In this paper wavelet time–frequency analysis is used to extract useful information from the clinical signals, since they are time-varying and mark important changes in patient’s response to drug dose. Model based predictive control algorithms are employed to regulate the depth of sedation by manipulating these two drugs. The results of identification from real data and the simulation of the closed loop control performance suggest that the proposed approach can bring an improvement of 9% in overall robustness and may be suitable for clinical practice.

Fractional Dynamics of Computer Virus Propagation

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

Dynamical Analysis and Visualization of Tornadoes Time Series

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.

Fractional Dynamics in the Rayleigh's Piston

This paper studies the dynamics of the Rayleigh piston using the modeling tools of Fractional Calculus. Several numerical experiments examine the effect of distinct values of the parameters. The time responses are transformed into the Fourier domain and approximated by means of power law approximations. The description reveals characteristics usual in Fractional Brownian phenomena.

Fractional Dynamics Representation in the Pseudo Phase Plane

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

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.

Fractional State Space Analysis of Temperature Time Series

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system 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).