Related papers: Multi-stability in Doubochinski's Pendulum
We study the dynamics of a mechanical oscillator with linear and cubic forces -the Duffing oscillator- subject to a feedback mechanism that allows the system to sustain autonomous periodic motion with well-defined amplitude and frequency.…
We investigate the classical problem of motion of a mathematical pendulum with an oscillating pivot. This simple mechanical setting is frequently used as the prime example of a system exhibiting the parametric resonance phenomenon, which…
The effect of decaying oscillatory perturbations on autonomous Hamiltonian systems in the plane with a stable equilibrium is investigated. It is assumed that perturbations preserve the equilibrium and satisfy a resonance condition. The…
We investigate the dynamics of a soliton that behaves as an extended particle. The soliton motion in an effective bistable potential can be chaotic in a similar way as the Duffing oscillator. We generalize the concept of geometrical…
Various solutions are displayed and analyzed (both analytically and numerically) of arecently-introduced many-body problem in the plane which includes both integrable and nonintegrable cases (depending on the values of the coupling…
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
A pendulum prepared perfectly inverted and motionless is a prototype of unstable equilibria and corresponds to an unstable hyperbolic fixed point in the dynamical phase space. Unstable fixed points are central to understanding Hamiltonian…
An inhomogeneous Kaluza-Klein compactification to four dimensions, followed by a conformal transformation, results in a system with position dependent mass (PDM). This origin of a PDM is quite different from the condensed matter one. A…
For self-sustained oscillators subject to noise the coherence, understood as a constancy of the instantaneous oscillation frequency, is one of the primary characteristics. The delayed feedback has been previously revealed to be an efficient…
We consider theories with time-dependent Hamiltonians which alternate between being bounded and unbounded from below. For appropriate frequencies dynamical stabilization can occur rendering the effective potential of the system stable. We…
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…
The periodic modulation of an oscillator's frequency can lead to so-called parametric oscillations at half the driving frequency, which display bistability between two states whose phases differ by \pi. Such phase-locking bistability is at…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
Stationary states of overdamped anharmonic stochastic oscillators driven by L\'evy noise are typically multimodal. The very same situation is recorded for an underdamped L\'evy noise driven motion in single-well potentials with linear…
This paper deals with various cases of resonance, which is a fundamental concept of science and engineering. Specifically, we study the connections between periodic and unbounded solutions for several classes of equations and systems. In…
Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, from Taylor's diffusion in…
The problem analysis results made the author to draw a conclusion that the nature of the resonance frequency long-term instability and drift at harmonic excitation is related to the phase dynamics of the "atom + field" system in the small…
The Pomeranchuk instability, in which an isotropic Fermi surface distorts and becomes anisotropic due to strong interactions, is a possible mechanism for the growing number of experimental systems which display transport properties that…
We explore stability and instability of rapidly oscillating solutions $x(t)$ for the hard spring delayed Duffing oscillator $$x''(t)+ ax(t)+bx(t-T)+x^3(t)=0.$$ Fix $T>0$. We target periodic solutions $x_n(t)$ of small minimal periods…
We study the global boundedness of the solutions of a non-smooth forced oscillator with a periodic and real analytic forcing. We show that the impact map associated with this discontinuous equation becomes a real analytic and exact…