The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical pitchfork are identified; then Hopf bifurcation, relaxation oscillation, together transition from bifurcation to oscillation discussed.

In [1] the occurence of a Hopf bifurcation at steady-state cornering for two-wheel oversteering vehicle with brush model tyre forces was found and following bifurcating branch periodic solutions we observed Canard phenomenon relaxation oscillations, which are typical singularly perturbed systems. that article assumed simplicity, car's center mass lies street level. this presentation investigate...

The aim of this work is to establish that the bifurcation parameter value leading to a canard explosion in dimension two obtained by the so-called Geometric Singular Perturbation Method can be found according to the Flow Curvature Method. This result will be then exemplified with the classical Van der Pol oscillator.

Abstract Existing sounding rocket flight is probably disturbed by external factors, of which attitude lack automatic control function and trajectory not stable, thus the project designed a canard adjustable posture scheme based on PID algorithm, can effectively solve stability path anti-interference problem with high efficiency.

After reviewing a number of results from geometric singular perturbation theory, we discuss several approaches to obtain periodic solutions in a slow manifold. Regarding nonhyperbolic transitions we consider relaxation oscillations and canard-like solutions. The results are illustrated by prey-predator systems.

We demonstrate experimentally and theoretically the existence of canard orbits and excitable quasiharmonic limit cycles in the thermo-optical dynamics of semiconductor optical amplifiers. We also observe the phase locking of the noise-induced spikes to the small-amplitude Hopf quasiharmonic oscillations, recently predicted by Makarov, Nekorkin, and Velarde [Phys. Rev. Lett. 86, 3431 (2001)]].

<p style='text-indent:20px;'>A class of two-fast, one-slow multiple timescale dynamical systems is considered that contains the system ordinary differential equations obtained from seeking travelling-wave solutions to FitzHugh-Nagumo in one space dimension. The question addressed mechanism by which a small-amplitude periodic orbit, created Hopf bifurcation, undergoes rapid amplitude growt...

We present an efficient off-line divisible e-cash scheme which is truly anonymous without a trusted third party. This is the second scheme in the literature which achieves full unlinkability and anonymity, after the seminal work proposed by Canard and Gouget. The main trick of our scheme is the use of a bounded accumulator in combination with the classical binary tree approach. The aims of this...