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Modal linear stability analysis has proven very successful in the analysis of coherent structures of turbulent flows. Formally, it describes the evolution of a disturbance in the limit of infinite time. In this work we apply modal linear…
The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
Motivated by recent developments in ion trap design and fabrication, we investigate the stability of ion motion in asymmetrical, planar versions of the classic Paul trap. The equations of motion of an ion in such a trap are generally…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
We study radial oscillations of hybrid non-rotating neutron stars composed by a quark matter core and hadronic external layers. At first, we physically deduce the junction conditions that should be imposed between two any phases in these…
Power systems with a high penetration of renewable generation are vulnerable to frequency oscillation and voltage instability. Traditionally, the stability of power systems is considered either in terms of local stability or as an angle…
Clouds of cold neutral atoms driven by a coherent light beam in a ring cavity exhibit self-structured states transversely with respect to the beam axis due to optomechanical forces and the back action of the atomic structures on the beam.…
We have investigated the stability of a set of non-rotating anisotropic spherical models with a phase-space distribution function of the Osipkov-Merritt type. The velocity distribution in these models is isotropic near the center and…
Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…
We investigate the dynamical formation of nonlinear patterns in one-dimensional ring condensates under bichromatic periodic modulation of the interaction strength. The stability phase diagram of the condensate's homogeneous density state is…
We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the four dimensional spaces of section we use the method of color…
We study the phase-space behaviour of nearby trajectories in integrable potentials. We show that the separation of nearby orbits initially diverges very fast, mimicking a nearly exponential behaviour, while at late times it grows linearly.…
The thermomagnetic instability of the critical state in superconductors is analysed with account of the dissipation and dispersion. The possibility is demonstrated of the existance of a nonlinear shok wave describing the final stage of the…
We analyse a nonlinear QW model which can be experimentally implemented using the components of the electric field on an optical nonlinear Kerr medium, which translates into a rotation in the coin operator, with an angle which depends (in a…
We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…
The present contribution proves the asymptotic orbital stability of viscous regularizations of stable Riemann shocks of scalar balance laws, uniformly with respect to the viscosity/diffusion parameter $\epsilon$. The uniformity is…
This is an analytic study of the problem of transitions between normal and superconducting phases for a sample which encloses a magnetic flux. A preliminary study of this problem, based on numerical minimization of the free energy for a…
(abridged) The physics of the pulsar magnetosphere near the neutron star surface remains poorly constrained by observations. Nevertheless it is believed that large vacuum gaps exist in the magnetosphere, and a non-neutral plasma partially…