Related papers: Exploring the Collective Behavior on the One-dimen…
I derive a loop representation for the canonical and grand-canonical partition functions for an interacting four-component Fermi gas in one spatial dimension and an arbitrary external potential. The representation is free of the "sign…
We study the dynamical behaviour of the collective field of chaotic systems on small world lattices. Coupled neuronal systems as well as coupled logistic maps are investigated. We observe that significant changes in dynamical properties…
We consider the behavior of a collective variable in a complex system formed by a finite number of interacting subunits. Each of them is characterized by a degree of freedom with an intrinsic nonlinear bistable stochastic dynamics. The lack…
The behavior of two-dimensional coupled map lattices is studied with respect to the global stabilization of unstable local fixed points without external control. It is numerically shown under which circumstances such inherent global…
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…
We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as…
The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the…
In this paper we investigate how many periodic attractors maps in a small neighbourhood of a given map can have. For this purpose we develop new tools which help to make uniform cross-ratio distortion estimates in a neighbourhood of a map…
This paper concerns the development of partial and semi-partial measures of spatial associations in the context of multivariate spatial lattice data which describe global or local associations among spatially aggregated measurements for…
We study the transport dynamics of matter-waves in the presence of disorder and nonlinearity. An atomic Bose-Einstein condensate that is localized in a quasiperiodic lattice in the absence of atom-atom interaction shows instead a slow…
The collective modes of a familiar two-dimensional one-component-plasma with the repulsive logarithmic interaction between the particles are analysed using the quasi-crystalline approximation (QCA) combined with the molecular dynamic…
This work surveys the topological and statistical properties of real quadratic maps and investigates the complex quadratic maps under holomorphic and non-holomorphic singular perturbations.
We study the peculiarities of the solitary state appearance in the ensemble of nonlocally coupled chaotic maps. We show that nonlocal coupling and features of the partial elements lead to arising of multistability in the system. The…
We investigate the spatiotemporal dynamics of a lattice of coupled chaotic maps whose coupling connections are dynamically rewired to random sites with probability p, namely at any instance of time, with probability p a regular link is…
We report exact analytical expressions locating the $0\to1$, $1\to2$ and $2\to4$ bifurcation curves for a prototypical system of two linearly coupled quadratic maps. Of interest is the precise location of the parameter sets where…
We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give, for an…
The present paper is devoted to the study of space mappings, which are more general than quasiregular mappings. The questions of the behavior of differentiable mappings having the so--called $N,$ $N^{-1},$ $ACP$ and $ACP^{-1}$ -- properties…
We propose a lattice model for Dirac fermions which allows us to break the degeneracy of the node structure. In the presence of a random gap we analyze the scaling behavior of the localization length as a function of the system width within…
Collective diffusion coefficient in a two-dimensional lattice gas on a nonhomogeneous substrate is investigated using variational approach. Particles reside at adsorption sites with different well depths potentials and jump randomly between…
Kinetic magnetism is an iconic and rare example of collective quantum order that emerges from the interference of paths taken by a hole in a sea of strongly interacting fermions. Here the lattice topology plays a fundamental role, with odd…