Localization in a discrete system of oscillators refers to the partition of the population into a subset that oscillates at high amplitudes and another that oscillates at much lower amplitudes. Motivated by experimental results on the Belousov–Zhabotinsky reaction, which oscillates in the relaxation regime, we study a mechanism of localization in a discrete system of relaxation oscillators glob...

The "tea-cup" attractor of a classical prey-predator-superpredator food chain model is studied analytically. Under the assumption that each species has its own time scale, ranging from fast for the prey to intermediate for the predator and to slow for the superpredator, the model is transformed into a singular perturbed system. It is demonstrated that the singular limit of the attractor contain...

This paper introduces a semi-empirical model to predict the downwash gradient at horizontal tail of three-lifting-surface aircraft. The superposition principle applied well established formulations valid for two lifting surfaces is not reasonable approach calculate canard-wing-tail layout, and this demonstrates that such basic technique leads incorrect results. Therefore, an ad hoc prediction p...

Group signatures allow a group member to sign messages anonymously on behalf of the group and, if needed, a group authority is able to identify the signer. In most applications, groups are dynamic and the number of arrivals and departures is non-negligible. Group signature schemes must take into account this situation and deal with member revocation. Even if group signature schemes have been in...

In this paper, some new lemmas on asymptotic analysis are established. We apply an asymptotic method to study generalized two-dimensional singularly perturbed systems with one parameter, whose critical manifold has an m 2 2 thorder degenerate extreme point. Certain sufficient conditions are obtained for the existence of canard solutions, which are the extension and correction of some existing r...

We study systems which combine both oscillatory and excitable properties, and hence intrinsically possess two internal frequencies, responsible for standard spiking and for small amplitude oscillatory limit cycles (Canard orbits). We show that in such a system the effect of stochastic resonance can be amplified by application of an additional high-frequency signal, which is in resonance with th...

We study the bifurcations of slow-fast cycles with two canard points in singularly perturbed planar systems. After analyzing local dynamics lying on S-shaped critical manifolds, we give a sufficient condition under which there exist three hyperbolic limit bifurcating from some cycles. The proof is based geometric singular perturbation theory. Then, apply results to cubic Liénard equations quadr...