Related papers: Dynamics towards the Feigenbaum attractor
We analyze the properties of the self-similar network obtained from the trajectories of unimodal maps at the transition to chaos via the horizontal visibility (HV) algorithm. We first show that this network is uniquely determined by the…
The some dynamic properties of a random heteropolymer in the condensed state are studied in the mode coupling approximation. In agreement with recent report a dynamic friction increasing is predicted for the random heteropolymer with…
The dissipative dynamics anticipated in the proof of 't Hooft's existence theorem -- "For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization" -- is constructed here…
We consider a system of two coupled particles evolving in a periodic and spatially symmetric potential under the influence of external driving and damping. The particles are driven individually in such a way that in the uncoupled regime,…
In this paper, we consider three-dimensional dynamical systems, as for example the Lorenz model. For these systems, we introduce a method for obtaining families of two-dimensional surfaces such that trajectories cross each surface of the…
In this paper, exact Hausdorff dimension formulas for a class of self-affine attractors generated by affine Iterated Function Systems are derived. We consider systems containing an affine map whose $n$-th iterate is a similarity…
A doubly nonlinear parabolic equation of the form $\alpha(u_t)-\Delta u+W'(u)= f$, complemented with initial and either Dirichlet or Neumann homogeneous boundary conditions, is addressed. The two nonlinearities are given by the maximal…
The R\"ossler system is one of the best known chaotic dynamical systems, generating a chaotic attractor which, by the numerical evidence, arises by a period-doubling route to chaos. In this paper we state and prove a topological criterion…
We study long-time dynamics of a class of abstract second order in time evolution equations in a Hilbert space with the damping term depending both on displacement and velocity. This damping represents the nonlinear strong dissipation…
We consider the effect of atomic hydrogen exposure to a system of two undoped sheets of graphene grown near a silica surface (the first adsorbed to the surface and the second freestanding near the surface). In the absence of atomic hydrogen…
The so-called Fundamental Theorem of Dynamical Systems -- which(1) relates attractors and repellers to the chain recurrent set and (2) gives the existence of a complete Lyapunov function -- can be seen as a means of separating out…
We study of the formation of pattern-forming fronts in the presence of a rigidly-propagating parameter ramp which is slowly-varying in space. In the context of the prototypical supercritical complex Ginzburg-Landau equation, we show that…
We consider the driven dynamics of a probe particle moving through an assembly of particles with competing long-range repulsive and short-range attractive interactions, which form crystal, stripe, labyrinth, and bubble states as the ratio…
The hydrodynamic attractors paradigm aims to explain the applicability of hydrodynamics after a very short timescale in ultra-relativistic nuclear collisions at RHIC and LHC in terms of the emergence of universal behavior across different…
A Lorenz map $f:[0,1]\to[0,1]$ is a piecewise continuous map, modeled after an idealized version of the Lorenz attractor. In this paper we settle the following question - how much of the dynamics of the Lorenz attractor can be modeled by…
We calculate rigorous bounds on the Hausdorff dimension of the attractor at the accumulation of the period-doubling cascade for families of maps with quadratic, cubic, and quartic critical point. To do this, we express the attractors as the…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
We discuss the collective dynamics of self-propelled particles with selective attraction and repulsion interactions. Each particle, or individual, may respond differently to its neighbors depending on the sign of their relative velocity.…
The interaction behavior of solitons are defining characteristics of these nonlinear, coherent structures. Due to recent experimental observations, thin ferromagnetic films offer a promising medium in which to study the scattering…
For systems with hidden attractors and unstable equilibria, the property that hidden attractors are not connected with unstable equilibria is now accepted as one of their main characteristics. To the best of our knowledge this property has…