Related papers: A new type of relaxation oscillation in a model wi…
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles…
We study a Cahn-Hilliard model for phase separation in composite materials with multiple periodic microstructures. These are modeled by considering a highly oscillating potential. The focus of this paper is in the case where the scales of…
The motion of a freely rotating prolate spheroid in a simple shear flow of a dilute polymeric solution is examined in the limit of large particle aspect ratio, $\kappa$. A regular perturbation expansion in the polymer concentration, $c$, a…
We consider the (noisy) Kuramoto model, that is a population of N oscillators, or rotators, with mean-field interaction. Each oscillator has its own randomly chosen natural frequency (quenched disorder) and it is stirred by Brownian motion.…
A system of autonomous differential equations with a stable limit cycle and perturbed by small white noise is analyzed in this work. In the vicinity of the limit cycle of the unperturbed deterministic system, we define, construct, and…
We consider the non linear focusing wave equation $\partial_{tt}u-\Delta u-u|u|^{p-1}=0$ in large dimensions and for radially symmetric data, in the energy supercritical zone for p large enough. We construct finite time blow up solutions…
We consider dissipative dynamics of atoms in a strong standing laser wave and find a nonlinear dynamical effect of synchronization between center-of-mass motion and internal Rabi oscillations. The synchronization manifests itself in the…
Wrinkling, creasing and folding are frequent phenomena encountered in biological and man-made bilayers made by thin films bonded to thicker and softer substrates often containing fibers. Paradigmatic examples of the latter are the skin, the…
Using numerical simulation methods and analytical approach, we demonstrate hard self-oscillation excitation in systems with infinitely many equilibrium points forming a line of equilibria in the phase space. The studied bifurcation…
This paper studies a slow-fast system whose principal characteristic is that the slow manifold is given by the critical set of the cusp catastrophe. Our analysis consists of two main parts: first, we recall a formal normal form suitable for…
In this paper, we consider the family of planar piecewise linear differential systems with two zones separated by a straight line without sliding regions, that is, differential systems whose flow transversally crosses the switching line…
We study the weakly nonlinear saturation of the flutter instability of a planar Cosserat rod in a viscous fluid driven by a terminal follower force. This instability, established in our preceding work as a Hopf bifurcation of a…
A variational framework is developed to examine the equilibrium states of a semi-flexible polymer that is constrained to lie on a fixed surface. As an application the confinement of a closed polymer loop of fixed length $2\pi R$ within a…
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…
Equilibrium states of a closed semiflexible polymer binding to a cylinder are described. This may be either by confinement or by constriction. Closed completely bound states are labeled by two integers: the number of oscillations, $n$, and…
The way granular materials response to an applied shear stress is of the utmost relevance to both human activities and natural environment. One of the their most intriguing and less understood behavior, is the stick-instability, whose most…
Bursting is a periodic transition between a quiescent state and a state of repetitive spiking. The phenomenon is ubiquitous in a variety of neurophysical systems. We numerically study the dynamical properties of a normal form of subcritical…
In classical mechanics, a light particle bound by a strong elastic force just oscillates at high frequency in the region allowed by its initial position and velocity. In quantum mechanics, instead, the ground state of the particle becomes…
The mechanism of the exponential transient statistics of Poincar\'e recurrences in the presence of chaos border with its critical structure is studied using two simple models: separatrix map and the kicked rotator ('microtron'). For the…
We discover a new Poincar\'e type phenomenon by establishing an optimal rigidity theorem for local CR mappings between circle bundles that are defined in a canonical way over (possibly reducible) bounded symmetric domains. We prove such a…