Related papers: Dynamics towards the Feigenbaum attractor
We analyze the motion of individual beads of a polymer chain using a discrete version of De Gennes' reptation model that describes the motion of a polymer through an ordered lattice of obstacles. The motion within the tube can be evaluated…
Slow adaption processes, like synaptic and intrinsic plasticity, abound in the brain and shape the landscape for the neural dynamics occurring on substantially faster timescales. At any given time the network is characterized by a set of…
We introduce a one-parameter family of polymatrix replicators defined in a three-dimensional cube and study its bifurcations. For a given interval of parameters, this family exhibits suspended horseshoes and persistent strange attractors.…
We study the origin of attracting phenomena in the ray dynamics of coupled optical microcavities. To this end we investigate a combined map that is composed of standard and linear map, and a selection rule that defines when which map has to…
Non-equilibrium self-organized patterns formed by particles interacting through competing range interaction are driven over a substrate by an external force. We show that, with increasing driving force, the pre-existed static patterns…
We study a two-parameter family of one-dimensional maps and related (a,b)-continued fractions suggested for consideration by Don Zagier. We prove that the associated natural extension maps have attractors with finite rectangular structure…
A geometric formulation of the linear beam dynamics in accelerator physics is presented. In particular, it is proved that the linear transverse and longitudinal dynamics can be interpret geometrically as an approximation to the Jacobi…
In a previous paper we considered a sequence of maps on a complete metric space $(X,d)$ and derived an extension of the Banach fixed point theorem. We showed that backward trajectories of maps $X\to X$ converge under mild conditions and…
We clarify the connection between attractor solutions known from studies of Bjorken flow in conformal models of relativistic fluid dynamics and the more general description of attractors as submanifolds in phase space. We show how to…
We study the dynamics of the periodically-forced May-Leonard system. We extend previous results on the field and we identify different dynamical regimes depending on the strength of attraction $\delta$ of the network and the frequency…
We propose a theoretical framework for an explanation of the numerically discovered phenomenon of the attractor-repeller merger. We identify regimes which are observed in dynamical systems with attractors as defined in a work by Ruelle and…
The topological structure of basin boundaries plays a fundamental role in the sensitivity to the initial conditions in chaotic dynamical systems. Herewith we present a study on the dynamics of dissipative systems close to the Hamiltonian…
In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of…
We study dynamical properties of generalized Bowen-Series boundary maps associated to cocompact torsion-free Fuchsian groups. These maps are defined on the unit circle (the boundary of the Poincar\'e disk) by the generators of the group and…
In this paper we explore the features of a graph generated by random walkers with nodes that have evolutionary attractiveness and Boltzmann-like transition probabilities that depend both on the euclidean distance between the nodes and on…
This paper concerns the dynamical behavior of weakly reversible, deterministically modeled population processes near the facets (codimension-one faces) of their invariant manifolds and proves that the facets of such systems are "repelling."…
On a lattice, as the momentum space is compact, the kinetic energy is bounded not only from below but also from above. It is shown that this, somehow removes the distinction between repulsive and attractive forces. In particular, it is seen…
As a counterpart to our previous study of the stationary distribution formed by sums of positions at the Feigenbaum point via the period-doubling cascade in the logistic map (Eur. Phys. J. B 87 32, (2014)), we determine the family of…
The dynamics of the web map with weak linear dissipation is studied. The evolution of the coexisting attractors and the structure of their basins while changing the dissipation and nonlinearity are revealed. It is shown that the structure…
According to the theory of relativity, the relativistic Coulomb's force between an electron pair is composed of two parts, the main part is repulsive, while the rest part can be attractive in certain situations. Thus the relativistic…