José Roberto Castilho Piqueira

A modified epidemiological model for computer viruses

Since the computer viruses pose a serious problem to individual and corporative computer systems, a lot of effort has been dedicated to study how to avoid their deleterious actions, trying to create anti-virus programs acting as vaccines in personal computers or in strategic network nodes. Another way to combat viruses propagation is to establish preventive policies based on the whole operation of a system that can be modeled with population models, similar to those that are used in epidemiological studies. Here, a modified version of the SIR (Susceptible-Infected-Removed) model is presented and how its parameters are related to network characteristics is explained. Then, disease-free and endemic equilibrium points are calculated, stability and bifurcation conditions are derived and some numerical simulations are shown. The relations among the model parameters in the several bifurcation conditions allow a network design minimizing viruses risks.

Dynamic models for computer viruses

Computer viruses are an important risk to computational systems endangering either corporations of all sizes or personal computers used for domestic applications. Here, classical epidemiological models for disease propagation are adapted to computer networks and, by using simple systems identification techniques a model called SAIC (Susceptible, Antidotal, Infectious, Contaminated) is developed. Real data about computer viruses are used to validate the model.

Analyzing the effect of the phase-jitter in the operation of second order phase-locked loops

Phase-locked loops (PLLs) are designed to extract timing signals in telecommunication networks. Noise, cross-talk, inter-symbol interference, quantization noise, and signal distortion are responsible for oscillations in the time between two successive transitions of the clock or data signal. It appears as an accidental phase modulation superposed to the original signal. This phenomenon is called timing jitter and affects the integrity of the data recovering process and, as a consequence, the error bit rate is increased. This problem has been studied by treating the jitter as a band limited noise process and tolerance masks for the jitter amplitude and frequency are recommended for several network architectures. Here, we develop a simple model with the continuous phase deviations of the clock signals considered as periodic signals in the band of the real disturbances. Comparisons with the stochastic approach are presented.

Bifurcation analysis for third-order phase-locked loops

Second-order phase-locked loops (PLLs) are extensively used in applications related to recovering clock signals for synchronous demodulation in telecommunication networks. In situations where an improvement of the transient response of the local clocks is necessary, third-order PLLs are employed. Here, we use concepts taken from dynamical system theory for analytically determining the capture range of three nonlinear third-order PLLs subject to a ramp input. We show that saddle-node, saddle-saddle, and Hopf bifurcations can be produced by varying the values of the input signal velocity and of the PLL parameters, providing criteria for designing such PLLs.

Computing with phase locked loops: choosing gains and delays

We simulate a four-node fully connected phase-locked loop (PLL) network with an architecture similar to the neural network proposed by Hoppensteadt and Izhikevich (1999, 2000), using second-order PLLs. The idea is to complement their work analyzing some engineering questions like:how the individual gain of the nodes affects the synchronous state of whole network; how the individual gain of the nodes affects the acquisition time of the whole network; how close the free-running frequencies of the nodes need to be in order to the network be able to acquire the synchronous state; how the delays between nodes affect the synchronous state frequency. The computational results show that the Hoppensteadt-Izhikevich network is robust to the variation of these parameters and their effects are described through graphics showing the dependence of the synchronous state frequency and acquisition time with gains, free-running frequencies, and delays.

Two-way master-slave double-chain networks: limitations imposed by linear master drift for second order PLLs as slave nodes

Distribution of precise time signals among the nodes of a network is a fundamental requirement for digital transmission and switching systems in telecommunication and control. Cideciyan et al., (1987) conjectured that two-way master-slave (TWMS) networks present, in the general case, a better performance than one-way master-slave (OWMS) considering the long term linear master frequency drift. In this work we study the TWMS case using dynamical system theory showing that, due to the effects of long-term clock instabilities, the steady-state frequency-error is unstable for a number of slaves higher or equal than four, limiting the use of this kind of architecture.

Global and partial synchronism in phase-locked loop networks

We analytically investigate the existence of global and partial synchronism in neural networks where each node is represented by a phase oscillator. Partial synchronism, which is important to pattern recognition, can be caused by increasing the natural frequency of an oscillator and restricting the frequencies of others in certain ranges.

Application of passive control to energy harvester efficiency using a nonideal portal frame structural support system

An analysis of a new energy harvester model is presented, based on a simple portal frame structure, considered a nonideal system due to the kind of excitation influenced by the response of the system, such as a direct current motor with limited power supply. The horizontal motion of the portal frame is considered under a nonideal excitation, and the approximated mathematical model of the system is obtained, considering the coupled oscillators. To model the piezoelectric coupling, the nonlinearities of the piezoelectric material were considered. A constantly sustained energy harvesting is essential for using these devices in real applications; for this, a control strategy is required. Passive control was obtained by means of a nonlinear substructure with properties of nonlinear energy sink. Numerical simulations were performed in order to find best values of control parameters. To check the robustness of the control strategy, an analysis considering uncertainties in the parameters of the model was performed, showing the efficiency of the passive control (energy pumping) in the suppression of the chaotic behavior, as well as the sensitivity of the control system to parametric errors. Passive control leads the system to a stable periodic orbit, allowing a more efficient energy harvest, due to the higher peak-to-peak amplitude of oscillation mean value. The passive control strategy eliminates the need for an active microcontroller to stabilize the system in a periodic orbit, improving the energy budget (harvested versus expended). The results show the displacement of the structure and the maximum power harvested by the device with and without passive nonlinear energy sink. It can be concluded that the application of passive control was successful. The control was robust and improved the energy harvested through the suppression of the chaotic motion, leading the system to a periodic orbit with stable amplitude of vibration, without damaging the structure.

Modeling and Filtering Double-Frequency Jitter in One-Way Master–Slave Chain Networks

One-way master-slave (OWMS) chain networks are widely used in clock distribution systems due to their reliability and low cost. As the network nodes are phase-locked loops (PLLs), double-frequency jitter (DFJ) caused by their phase detectors appears as an impairment to the performance of the clock recovering process found in communication systems and instrumentation applications. A nonlinear model for OWMS chain networks with P+1 order PLLs as slave nodes is presented, considering the DFJ. Since higher order filters are more effective in filtering DFJ, the synchronous state stability conditions for an OWMS chain network with third-order nodes are derived, relating the loop gain and the filter coefficients. By using these conditions, design examples are discussed.

Rumor Propagation Model: An Equilibrium Study

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.