Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert’s 16th problem [Hilbert, 1900, Hilbert, 1902], are still open for this family. In this article we make a global study of the familyQTN ...

The study of planar quadratic differential systems is very important not only because they appear in many areas of applied mathematics but due to their richness in structure, stability and questions concerning limit cycles, for example. Even though many papers have been written on this class of systems, a complete understanding of this family is still missing. Classical problems, and in particu...

Recent experiments have explored the response of a single modeoptically injected QD laser. The experiments identify a domain ofbistability between two steady states at negative detuning and a Hopfbifurcation close to the locking threshold at positive detuning. More-over, the laser is stable for all injection levels at zero detuning. Theseobservations lead to a stability ...

In this paper, we build a model of energy-savings and emission-reductions with two delays. In this model, it is assumed that the interaction between energy-savings and emission-reduction and that between carbon emissions and economic growth are delayed. We examine the local stability and the existence of a Hopf bifurcation at the equilibrium point of the system. By employing System Complexity T...

We compare the dynamics of the periodically forced FitzHugh-Nagumo oscillator in its relaxation regime to that of a one-dimensional discrete map of the circle derived from the phase-resetting response of this oscillator (the "phase-resetting map"). The forcing is a periodic train of Gaussian-shaped pulses, with the width of the pulses much shorter than the intrinsic period of the oscillator. Us...

2014 We investigate the stability of the planar front during directional solidification of a quasi-azeotrope. We show that the corresponding shape of the phase diagram induces a strong reduction of the scale of the bifurcation curve which makes its complete exploration feasible in standard directional solidification experiments. We show that the finite concentration of azeotropic mixtures resul...