We consider an ordinary differential equation model for neural competition, presented previously in the study of binocular rivalry, which features two adapting populations of neurons interacting through mutual inhibition. This model is known to exhibit a variety of dynamic regimes, including mixed-mode oscillations (MMOs) featuring alternating small and large amplitude oscillations, depending o...

We consider here a model from [1] for regenerative chatter in a drilling process. The model is a nonlinear delay differential equation where the delay arises from the fact that the cutting tool passes over the metal surface repeatedly. For any fixed value of the delay, a large enough increase in the width of the chip being cut results in a Hopf bifurcation from the steady state, which is the or...

The complexity of voting procedures make it challenging to design a secure electronic voting system. In many proposals, the security of the system relies mainly on a black box voting machine. Meanwhile, the most advanced proposals base their security arguments on (complicated) cryptographic protocols, e.g. blind signatures or homomorphic schemes. Canard and Traoré proposed cryptographic primiti...

We consider the effect of Gaussian white noise on fast–slow dynamical systems with one fast and two slow variables, containing a folded-node singularity. In the absence of noise, these systems are known to display mixed-mode oscillations, consisting of alternating largeand small-amplitude oscillations. We quantify the effect of noise and obtain critical noise intensities above which the small-a...

We study the dynamics of a circadian oscillator model proposed by Tyson, Hong, Thron and Novak. This describes molecular mechanism for rhythm in Drosophila. After giving detailed its equilibria, we investigate cases that rate mRNA degradation is sufficiently high or low. When high, prove there are no periodic orbits region with biological meaning. low, this transformed into slow–fast system. Th...

Notwithstanding the interest in three-surface concept shown by aircraft designers, this configuration was not thoroughly investigated conjunction with adoption of two-elevator surfaces, on both canard and tail. In fact, inclusion an additional elevator produces a redundant longitudinal control which can be specifically exploited to target trim optimization. The same redundancy also employed imp...