Showing papers in "Physica D: Nonlinear Phenomena in 2013"

TL;DR: In this paper, a general framework for the definition and computation of the isostables of stable fixed points is provided, which is based on the spectral properties of the Koopman operator.

TL;DR: In this article, the Hartman-Grobman Theorem is extended to the basin of attraction, for both discrete diffeomorphisms and flows, and the connection of the linearizing transformation to the spectrum of Koopman operator is discussed.

TL;DR: In this article, a new analytic transfer operator construction that enables the calculation of finite-time coherent sets (sets are that minimally dispersive over a finite time interval) is introduced.

TL;DR: In this paper, a coarse-grained method based on Favre filtering was proposed to analyze highly compressible turbulence, and it was shown that the requirement that viscous effects on the dynamics of large-scale momentum and kinetic energy be negligible, an inviscid criterion, naturally supports a density weighted coarsegraining of the velocity field.

TL;DR: In this article, the authors investigated nonlocal interaction equations with repulsive-attractive radial potentials and proved that under some conditions on the potential, radially symmetric solutions converge exponentially fast in some transport distance toward a spherical shell stationary state.

TL;DR: The results show how epidemic risk and population movement affect the spatial distribution of infectious disease and thereby suggest important implications for predicting the patterns of disease occurrence and designing optimal control strategies.

TL;DR: In this article, the authors considered the aggregation equation ρ t − ∇ ⋅ ( ρ ∇ K ∗ ρ ) = 0 in R n, where the interaction potential K incorporates short-range Newtonian repulsion and long-range power-law attraction.

TL;DR: This special issue grew out of a BIRS workshop of the same title and contains new research contributions from a broad spectrum of researchers on topics related to emergent behaviour to showcase the diversity and vitality of this area and serve as a useful resource for future reference.

TL;DR: In this article, a modified quasilinear Gaussian (MQG) closure is developed in two stages to decompose the energy flux at equilibrium into precise additional damping and enhanced noise on suitable modes, while preserving statistical symmetries.

TL;DR: In this paper, the spectral and nonlinear stabilities of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation are investigated. But the spectral analysis is based on detailed estimates of the linearized solution operator, which are complicated by the fact that the spectrum of the associated linearization intersects the imaginary axis at the origin.

TL;DR: In this paper, the authors introduce a Cucker-Smale-type model for flocking, where the strength of interaction between two agents depends on their relative separation (called "topological distance") which is the number of intermediate individuals separating them.

TL;DR: In this paper, the existence of a traveling breather in a Fermi-Pasta-Ulam lattice was shown for a class of beads interacting via Hertz's contact forces, and the authors considered the setting in which an additional onsite potential is present, motivated by the Newton's cradle under the effect of gravity.

TL;DR: This paper presents two methods of realising arbitrarily complex directed graphs as robust heteroclinic networks for flows generated by ODEs and realises the graph as an invariant set within an attractor, and discusses some illustrative examples.

TL;DR: In this article, the Sakaguchi-Kuramoto model of coupled phase oscillators in a continuum limit given by a frequency dependent version of the Ott-Antonsen system is analyzed.

TL;DR: In this article, the authors introduce two new approaches based on singular value decomposition and exponential dichotomies and comparatively review and improve two recent popular approaches of Ginelli et al. (2007) and Wolfe and Samelson (2007).

TL;DR: In this article, the authors consider a self-propelled particle system which has been used to describe certain types of collective motion of animals, such as fish schools and bird flocks, and introduce a class of interaction potentials, that are called quasi-Morse, for which flock and rotating mill states are also observed numerically, however in that case the corresponding macroscopic equations allow for explicit solutions in terms of special functions, with coefficients that can be obtained numerically without solving the particle evolution.

TL;DR: In this article, the authors investigated stationary, spatially localised crime hotspots on the real line and the plane of an urban crime model of Short et al. and showed that the bifurcating pulses can undergo the process of homoclinic snaking near the singular limit.

TL;DR: In this paper, an extension of a previously developed population model based on the well-known diffusive logistic equation with nonlocal interaction, to a system involving competing species, is presented.

TL;DR: In this article, a simplified model of the gravitational instability of an initially homogeneous infinite medium, represented by T d, based on the approximation that the mean fluid velocity is always proportional to the local acceleration, is studied.

TL;DR: In this article, the coefficients of the powers of e in the series expansion of the solutions around e = 0 of the perturbed first-order differential equations are given. And an averaging theory at any order in e for the following two kinds of analytic differential equations is given.

TL;DR: In this article, the spectral stability properties of periodic traveling waves in the sine-Gordon equation were studied, including wave types of both subluminal and superluminous propagation velocities as well as waves of both librational and rotational types.

TL;DR: In this article, a general family of nonlinear phase oscillators which can exhibit arbitrary limit cycle shapes and infinitely large basins of attraction is presented, based on morphing the limit cycle of an existing phase oscillator with phase-based scaling functions to obtain a desired limit cycle behavior.

TL;DR: In this article, the formation of singularities in solutions to the dispersionless Kadomtsev-Petviashvili (dKP) equation is studied numerically for different classes of initial data.

TL;DR: In this article, the authors considered the case of two weakly coupled identical Hamiltonian oscillators in resonance and showed that any amount of energy imparted to one of the oscillators gets transferred back and forth between these oscillators with a frequency proportional to the coupling.

TL;DR: In this article, the spectral stability of tetrahedral orbits of the corresponding 4-body problem in the 2-dimensional case was studied. But the authors focused on the 3-body case.

TL;DR: This work compute the most probable transition path of stochastic equations by minimizing the effective action in a corresponding deterministic Hamiltonian system by using an iterative scheme for solving a two-point boundary value problem for theHamiltonian system.

TL;DR: Results are described showing that, in the small observational noise limit, the filters can be tuned to perform accurately in tracking the signal itself (filter accuracy), provided the system is observed in a sufficiently large low dimensional space; roughly speaking this space should be large enough to contain the unstable modes of the linearized dynamics.

TL;DR: The cumulative effects of errors of (short-term) wind field forecasts on the finite-time Lyapunov exponent (FTLE) fields and the associated LCSs when realistic forecast plans impose certain limits on the forecasting parameters are revealed.

TL;DR: In this article, the authors exploit the large value of the slope parameter to obtain leading order approximations to the parameter regions in which patterns exist, and to the form of these patterns.

TL;DR: In this article, the problem of growing complexity of the dynamics of the coupled phase oscillators as the number of oscillators in the chain increases is considered and the organization of the parameter space (parameter of the frequency detuning between the second and the first oscillators versus parameter of dissipative coupling) is discussed.