Optimal control measures for a susceptible-carrier-infectious-recovered-susceptible malware propagation model

Purposing to lessen malware propagation, this paper proposes optimal control measures for a susceptible-carrier-infectious-recovered-susceptible (SCIRS) epidemiological model formed by a system of ordinary differential equations. By taking advantage of real-world data related to the number of reported cybercrimes in Japan from 2012 to 2017, an optimal control problem is formulated to minimize the number of infected devices in a cost-effective way. The existence and uniqueness of the results related to the optimality system are proved. Overall, numerical simulations show the usefulness of the proposed control strategies in reducing the spread of malware infections.- Fundação para a Ciência e Tecnologia, Grant/Award Number: UID/MAT/04106/2019 and UID/CEC/00319/201

Symmetric bifurcation analysis of synchronous states of time-delayed coupled Phase-Locked Loop oscillators

In recent years there has been an increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry patterns can emerge in these networks, as a consequence a part of the system might repeat itself, and properties of this subsystem are representative of the dynamics on the whole phase space. In this paper an analysis of the second order N-node time-delay fully connected network is presented which is based on previous work: synchronous states in time-delay coupled periodic oscillators: a stability criterion. Correa and Piqueira (2013), for a 2-node network. This study is carried out using symmetry groups. We show the existence of multiple eigenvalues forced by symmetry, as well as the existence of Hopf bifurcations. Three different models are used to analyze the network dynamics, namely, the full-phase, the phase, and the phase-difference model. We determine a finite set of frequencies ω, that might correspond to Hopf bifurcations in each case for critical values of the delay. The S map is used to actually find Hopf bifurcations along with numerical calculations using the Lambert W function. Numerical simulations are used in order to confirm the analytical results. Although we restrict attention to second order nodes, the results could be extended to higher order networks provided the time-delay in the connections between nodes remains equal. © 2014 Elsevier B.V. All rights reserved

Using Shannon entropy on measuring the individual variability in the Rufous-bellied thrush Turdus rufiventris vocal communication

We applied the information theory concepts to notes repertoire characteristics combined with temporal parameters of the Rufous-bellied thrush Turdus rufiventris song, using this particular case to test a new method of analysing quantitatively complex animal communication systems. Like most Turdus thrushes, Rufous-bellied thrushes are remarkable for their long, varied and melodious songs. For the analysis of the species repertoire, we used recordings of 44 individuals from 24 localities covering its full geographical range. We measured the repertoire size, note duration and rhythm (frequency of note utterance), and combined these parameters with the Shannon entropy values calculated for each individual. Although individuals maintain species-specific recognition capacity, we find a large variation between their song parameters and show that the information theory can be useful to analyse large and varied animal vocal repertoires. We are introducing two new parameters, temporal average entropy (E-t) and utterance frequency average entropy (E-f), for measuring such communication systems. (C) 2000 Academic Press.2071576

Measuring q-bits in three-trophic level systems

The use of quantum information has been proposed as an approach to deal with biological data (Piqueira, J.R.C., Serboncini, F.A., Monteiro, L.H.A., 2006. Biological models: measuring variability with classical and quantum information. J. Theor. Biol. 242 (2), 309-313). Using three-trophic level systems as examples, we show how to model population data by expressing the system states with q-bits. The system time evolution is given by the state transition matrices which relate the states to successive time intervals. It is a complementary way of looking at the problem which is usually modeled with deterministic differential equations. This is possible because the dynamics of interacting populations in three-trophic level systems is a problem with several coupled variables and, consequently, complex dynamical behaviors seem to result. The non deterministic dynamics generated by the state transition matrices is supposed to model the biological system as a whole, with real data expressing even the global effects of small disturbances in the ecological parameters. (c) 2006 Elsevier B.V. All rights reserved.2004167118318