Showing papers in "Physica D: Nonlinear Phenomena in 2009"

TL;DR: In this article, the authors discuss the early history of the field of modulation instability in modern theory of nonlinear waves, and demonstrate how scientific demand resulted in independent and almost simultaneous publications by many different authors on modulation instability, a phenomenon resulting in a variety of non-linear processes such as envelope solitons, envelope shocks, freak waves, etc.

TL;DR: In this paper, a variety of mixed synchronous/incoherent (chimera) states in several heterogeneous networks of coupled phase oscillators are studied, where the Ott-Antonsen ansatz is used to reduce the number of variables in the partial differential equation governing the evolution of the probability density function by one, resulting in a time-evolution PDE for a variable with as many spatial dimensions as the network.

TL;DR: In this paper, the authors study the transport and mixing properties of flows in a variety of settings, connecting the classical geometrical approach via invariant manifolds with a probabilistic approach via transfer operators.

TL;DR: In this article, a decomposition of the solution field into a mean and stochastic dynamical component is derived from the original SPDE, using nothing more than a dynamically orthogonal condition on the representation of a solution.

TL;DR: A general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models to cover: nonlinear evolution and observation functions, unknown parameters and (precision) hyperparameters and model comparison and prediction under uncertainty is described.

TL;DR: In this paper, the authors study the consensus problems for a group of interacting agents and prove that the agents of the group under a particular type of nonlinear interaction can reach the consensus state in finite time in the scenarios with fixed and switching undirected topologies.

TL;DR: This work presents sufficient conditions for synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions using the theory of semi-passive and passive systems and demonstrates that when the coupling is strong enough the oscillators become synchronized.

TL;DR: In this paper, localised patterns emerging from a subcritical modulation instability are analyzed by carrying the multiple-scales analysis beyond all orders, and the full bifurcation diagram is computed analytically.

TL;DR: In this article, complex damped and undamped dynamics and targeted energy transfers (TETs) in systems of coupled oscillators, consisting of single-degree-of-freedom primary linear oscillators (LOs) with vibroimpact attachments, acting, in essence, as vibro-impact nonlinear energy sinks (VI NESs), are investigated.

TL;DR: In this article, the authors used experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer and trimer cell structures in one-dimensional granular lattices.

TL;DR: In this article, a detailed study of the local and global bifurcations of codimension one and two of limit cycles is performed, which provides us a global idea of the three-parametric evolution of the system.

TL;DR: In this article, it was shown that Bose-Einstein condensates in a honeycomb optical lattice can be described by a nonlinear Dirac equation in the long wavelength, mean field limit.

TL;DR: In this paper, a hydrodynamic system was established to study vesicle deformations under external flow fields, in the Eulerian formulation, involving the coupling of the incompressible flow system and a phase field equation.

TL;DR: In this article, a minimal model of a population of identical oscillators with a nonlinear coupling is presented, which is a generalization of the popular Kuramoto model, and the analysis based on the Watanabe-Strogatz ansatz allows us to describe the self-organized bunch states in any finite ensemble as a set of equilibria.

TL;DR: In this paper, the ensemble unscented Kalman filter (EnUKF) was proposed to estimate the ensemble mean and covariance of the background by examining the multidimensional Taylor series expansion term by term.

TL;DR: In this paper, the authors used the Poincare compactification for polynomial vector fields in R 3 to study the dynamics of the Rikitake system at infinity, showing that there are orbits which escape to, or come from, infinity, instead of going towards the attractor.

TL;DR: In this paper, the synchronization in the system of coupled non-identical non-isochronous van der Pol-Duffing oscillators with inertial and dissipative coupling is discussed.

TL;DR: This paper addresses the robustness of synchronization in the presence of parameter mismatches between the coupled circuits in the case of hyperchaotic behavior and proposes a master–slave scheme based on negative feedback.

TL;DR: In this article, the authors discuss partial synchronization of linearly and symmetrically coupled ODEs via invariant synchronization manifolds, and investigate how topological structure affects partial synchronization, and give a valuable discussion about the possibility of partial synchronization with increasing coupling strength.

TL;DR: In this paper, the existence, stability, and mobility of fundamental discrete solitons in two-and three-dimensional nonlinear Schrodinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities were investigated.

TL;DR: In this paper, the formation of the Van Dommelen and Shen singularity in the complex plane has been studied using the singularity tracking method and it has been shown that the van-dommelen singularity is a cubic root singularity.

TL;DR: In this article, the dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied and asymptotic expressions for boundaries of instability domains near resonance frequencies are derived.

TL;DR: In this paper, the authors examined the lower bound of the net driving power of a controlled duct flow under a constant flow rate, and showed that the upper bound is given by the dissipation rate of the Stokes flow at the same flow rate.

TL;DR: In this article, the authors introduce a new notion of linear stability for standing waves of the nonlinear Schrodinger equation (NLS) which requires not only that the spectrum of the linearization be real, but also that the generalized kernel be not degenerate and that the signature of all the positive eigenvalues be positive.

TL;DR: In this article, the impact of sub-threshold periodic pacemaker activity and internal noise on the spatial dynamics of excitable media was studied. But the authors focused on the dynamics of the pacemaker itself and not on the internal noise.

TL;DR: In this paper, a robust numerical algorithm to compute the Maslov index, to understand its properties, and to study the implications for the stability of solitary waves was developed in the exterior algebra representation.

TL;DR: Benney and Saffman as discussed by the authors analyzed the evolution of the cumulants of the random wave as originally formulated by D.J. Benney and P.C. Newell and provided a self-consistent weak-turbulence theory of the condensation process, in which the nonequilibrium formation of the Condensate is a natural consequence of the spontaneous regeneration of a non-vanishing first-order cumulant in the hierarchy of the Cumulants' equations.

TL;DR: In this article, a nonlinear model which provides soliton scattering with amplitude changes was investigated, and the authors derived its N-soliton solutions through Hirota method, and by means of asymptotic analysis it was found that two-soliton scattering provided not only phase shifts but also amplitude changes for each soliton.

TL;DR: In this article, a new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems and a detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a population in the four main regimes dominated respectively by gain and competition, gain and cooperation, loss and competition and loss and cooperation.

TL;DR: In this paper, the relation between the centro-affine geometry of star-shaped planar curves and the projective geometry of parametrized maps into R P 1 was studied.