Autoresonance is a phase locking phenomenon occurring in nonlinear oscillatory system, which is forced by oscillating perturbation. Many physical applications of the autoresonance are known in nonlinear physics. The essence of the phenomenon is that the nonlinear oscillator selfadjusts to the varying external conditions so that it remains in resonance with the driver for a long time. This long ...

In [3], some multiplicity results for the forced oscillations of a mass point constrained on a sphere have been obtained. In particular, it was proved that a small periodic perturbation of a gravitation-like tangent vector field induces at least two forced oscillations. Such results depend strictly on the strong geometric properties of the sphere and cannot be (easily) extended to the general s...

Abstract We consider the propagation of stratified fluid through a contraction near resonance, for which the governing asymptotic equation is the forced KdV equation. Steady solutions of this equation are sought which have constant, but differing amplitudes upstream and downstream of the contraction, and for which leading order dispersive effects are retained. A numerical algorithm is outlined ...

We consider a forced harmonic oscillator at resonance with a nonlinear perturbation and obtain a sharp condition for the existence of unbounded motions. Such a condition is extended to the case of a semilinear vibrating string. AMS classification scheme numbers: 34C11, 35L05

Two-dimensional, incompressible, zero guide-field, nonlinear Hall-MHD ~magnetohydrodynamical! simulations are used to investigate the scaling of the rate of forced magnetic reconnection in the so-called Taylor problem. In this problem, a small-amplitude boundary perturbation is suddenly applied to a tearing stable, slab plasma equilibrium; the perturbation being such as to drive magnetic reconn...

We explore different two parametric families of quasi-periodically Forced Logistic Maps looking for universality and self-similarity properties. In the bifurcation diagram of the one-dimensional Logistic Map it is well known that there exist parameter values sn where the 2-periodic orbit is superattracting. Moreover, these parameter values lay between the parameters corresponding to two consecu...

We explore different two-parametric families of quasi-periodically Forced Logistic Maps looking for universality and self-similarity properties. In the bifurcation diagram of the one-dimensional Logistic Map, it is well known that there exist parameter values sn where the 2-periodic orbit is superattracting. Moreover, these parameter values lay between the parameters corresponding to two consec...