Related papers: Comment on ``Phase ordering in chaotic map lattice…
The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. For chaotic systems, there are two distinct regimes of either exponential or Gaussian overlap decay in time. We develop a semiclassical approach…
Recent investigations in nonlinear sciences show that not only hyperbolic but also mixed dynamical systems may exhibit exponential relaxation in the chaotic regime. The relaxation rates, which lead the decay of probability distributions and…
The long-term behaviour of dynamic systems can be classified in two different regimes, regular or chaotic, depending on the values of the control parameters, which are kept constant during the time evolution. Starting from slightly…
The ordering dynamics of the Higgs field is studied, using techniques inspired by the study of phase ordering in condensed matter physics, as a first step to understanding the evolution of cosmic structure through the formation of…
The nonlinear dynamics of a recently derived generalized Lorenz model (Macek and Strumik, Phys. Rev. E 82, 027301, 2010) of magnetoconvection is studied. A bifurcation diagram is constructed as a function of the Rayleigh number where…
Rajagopalan and Sabir [nlin.CD/0104021 and Phys. Rev. E 63, 057201 (2001)] recently discussed deterministic diffusion in a piecewise linear map using an approach developed by Fujisaka et al. We first show that they rederived the random walk…
We investigate the dynamic phase transition from partially or fully arrested state to spatiotemporal chaos in coupled logistic maps on a small-world network. Persistence of local variables in coarse grained sense acts as an excellent order…
The paper explores the effect of random parameter switching in a fractional order (FO) unified chaotic system which captures the dynamics of three popular sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors. The…
We study the effects of phase-frustrated, higher-order interactions in a system of coupled phase oscillators with two communities. We use dimensionality reduction techniques to derive a low-dimensional system of ODEs to describe the…
Despite many attempts, ordered equilibrium microphases have yet to be obtained in experimental colloidal suspensions. The recent computation of the equilibrium phase diagram of a microscopic, particle-based microphase former [Zhuang et al.,…
We study numerically the disorder-induced localization-delocalization phase transitions that occur for mass and spring constant disorder in a three-dimensional cubic lattice with harmonic couplings. We show that, while the phase diagrams…
The phenomenon of synchronization occurring in a locally coupled map lattice subject to an external drive is compared to the synchronization process in an autonomous coupled map system with similar local couplings plus a global interaction.…
In systems exhibiting fluctuation-dominated phase ordering, a single order parameter does not suffice to characterize the order, and it is necessary to monitor a larger set. For hard-core sliding particles (SP) on a fluctuating surface and…
Self-adjusting, or adaptive systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these…
We discuss orientational order in two dimensions in the context of systems with competing isotropic interactions at different scales. We consider an extension of the Brazovskii model for stripe phases including explicitly quartic terms with…
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…
Unidirectionally coupled area-preserving maps with a mixed phase space may show identical synchronization in the sticky neighborhood of the regular islands. We use this fact to devise numerical procedures to control (delay and expedite) the…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
We numerically reexamine the scaling behavior of period doublings in four-dimensional volume-preserving maps in order to resolve a discrepancy between numerical results on scaling of the coupling parameter and the approximate…
This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result…