Jocirei D. Ferreira

Weak Allee effect in a predator-prey system involving distributed delays

In this paper we study the influence of weak Allee effect in a predator-prey system model. This effect is included in the prey equation and we determine conditions for the occurrence of Hopf bifurcation. The stability properties of the system and the biological issues of the memory and Allee models on the coexistence of the two species are studied. Finally we present some simulations which allow one to verify the analytical conclusions obtained. Mathematical subject classification: Primary: 34C25; Secondary: 92B05.

Symmetry-Breaking Bifurcations and Patterns of Oscillations in Rings of Crystal Oscillators

Symmetry is used to investigate the existence and stability of collective patterns of oscillations in rings of coupled crystal oscillators. We assume

Network of Coupled Oscillators for Precision Timing

N

Bifurcations of non-smooth systems

identical crystal oscillators, where each o...

Zip bifurcation in a competitive system with diffusion

Precise time dissemination and synchronization have been some of the most important technological tasks for several centuries. It was realized that precise time-keeping devices having the same stable frequency and precisely synchronized can have important applications in navigation. Satellite-based global positioning and navigation systems such as the GPS use the same principle. However, even the most sophisticated satellite navigation equipment cannot operate in every environment. In response to this need, we present a computational and analytical study of a network based model of a high-precision, inexpensive, Coupled Oscillator System and Timing device. Preliminary results from computer simulations seem to indicate that timing errors decrease as 1 / N when N crystals are coupled as oppose to \(1{/}\sqrt{N}\) for an uncoupled assemble. This manuscript is aimed, however, at providing a complete classification of the various patterns of collective behavior that are created, mainly, through symmetry-breaking bifurcations. The results should provide guidelines for follow-up simulations, design and fabrication tasks.