Vol. 3, No. 1 (2014): Regular Issue

Searching experiments conducted in different virtual environments over a gender balanced group of people revealed a gender irrelevant scale-free spread of searching activity on large spatiotemporal scales. The better per- formance of men in virtual environments can be associated with the reg- ularly renewed computer game experience, essentially in games played through a first-person perspective. We suggested a simple self-organized critical model of search, in which the experimentally observed scale-free behavior can be interpreted as a trade-off between the value of exploitation versus exploration amid uncertainty.

We reconsider the C. Peskin model of the cardiac pacemaker assuming that pulse-couplings are delayed. Sufficient conditions for synchronization of identical and non-identical oscillators are obtained. The results are demon- strated with numerical simulations.

In this paper, we study boundary value problems for impulsive fractional evolution integrodifferential equations with Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions. An example is given to illustrate the results.

In this paper, it is proposed a mathematical model for co-infection of HIV/AIDS and tuberculosis. The model includes treatment and vertical transmission for HIV/AIDS. The treatment for tuberculosis is not included. The disease-free equilibrium of the model is computed and local stability is proved. The reproduction numbers of the full model and of its two sub- models, concerning single infection by HIV/AIDS and single infection by tuberculosis, are also calculated. Numerical simulations show the effect of the variation of the recruitment rate, of the movement rate, and of the tuberculosis infection rate on the variables of the model. Results are as expected. Namely an increase in the recruitment rate increases the suscep- tible population. As the movement rate is decreased, the individuals single infected with HIV decrease. Moreover, an increase in the tuberculosis in- fection rate translates in an increase of the single infected with tuberculosis and dually-infected with tuberculosis and HIV/AIDS individuals. Future work will consider the inclusion of treatment of tuberculosis.

We study solvability in H2 of certain linear nonhomogeneous elliptic prob- lems involving the sum of the periodic Laplacian and a Schrödinger oper- ator without Fredholm property and prove that under reasonable technical conditions the convergence in L2 of their right sides implies the existence and the convergence in H2 of the solutions. We generalize the methods of spectral and scattering theory for Schro ̈dinger type operators from our preceding work [1].

Soliton lattices are periodic solutions of Ginzburg-Landau equation which can be useful tools to explore the coarsening process (or Ostwald ripening) which takes place during a Cahn-Hilliard dynamics.They can be used to identify the stationary solutions of the dynamics and how these intermedi- ate states are destroyed by fluctuations. The coarsening process drives the systems from a stationary solution to the next one which is of period double and of lower energy. Using another family of soliton lattices, this process can be described continuously via a phase field equation. We present here properties of these two families, including the Fourier series decomposition of the non symmetric soliton lattice which we use as building block of our ansatz.

In this paper, analytical solutions of periodic motions in a periodi- cally excited, time-delayed, quadratic nonlinear oscillator are obtained through the Fourier series, and the stability and bifurcation of such pe- riodic motions are discussed by eigenvalue analysis. The analytical bifurcation tree of period-1 motion to chaos in such a time-delayed, quadratic oscillator is presented through period-1 to period-8 motion. Numerical illustrations of stable and unstable periodic motions are given by numerical and analytical solutions. Compared to dynami- cal systems without time-delay, the time-delayed dynamical systems possess different periodic motions and the bifurcation trees of periodic motions to chaos are also distinguishing.