Related papers: Formation of localized structures in bistable syst…
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…
Optical systems that combine nonlinearity with coupling between various subsystems offer a flexible platform for observing a diverse range of nonlinear dynamics. Furthermore, engineering tolerances are such that the subsystems can be…
In this work we characterize the dynamical instabilities of localized structures exhibited by a recently introduced Gelens et al., Phys. Rev. A 75, 063812 2007 generalization of the Lugiato-Lefever model that includes a weakly nonlocal…
The possibility that extremely long-lived, time-dependent, and localized field configurations (``oscillons'') arise during the collapse of asymmetrical bubbles in 2+1 dimensional phi^4 models is investigated. It is found that oscillons can…
We study the properties of junctions created by crossing of N identical branches of linear discrete networks. We reveal that for N>2 such a junction creates a topological defect and supports two types of spatially localized modes. We…
In this work, we study the bifurcation structures and the stability of multidimensional localized states within coherently driven Kerr optical cavities with parabolic potentials in 1D, 2D, and 3D systems. Based on symmetric considerations,…
The dynamics of nonlocally coupled dissipative kicked rotors is rich and complex. In this study, we consider a network of rotors where each interacts equally with a certain range of its neighbors. We focus on the influence of the coupling…
We prove the existence of exponentially localised and time-periodic solutions in general nonlinear Hamiltonian lattice systems. Like normal modes, these localised solutions are characterised by collective oscillations at the lattice sites…
Complex structures often emerge from initially homogeneous or weakly correlated states. We address the apparent tension between this ordering and entropy growth through a unified framework combining semi-microscopic phase-space dynamics,…
We study transitions from convective to absolute instability near a trivial state in large bounded domains for prototypical model problems in the presence of transport and negative nonlinear feedback. We identify two generic scenarios,…
Formation of stationary localized states in one-dimensional chain as well as in a Cayley tree due to a linear impurity and a nonlinear impurity is studied. Furthermore, a one-dimensional chain with linear and nonlinear site energies at the…
This work studies front formation in the Allen-Cahn equation with a parameter heterogeneity which slowly varies in space. In particular, we consider a heterogeneity which mediates the local stability of the zero state and subsequent…
We study spatiotemporal chaos in two-dimensional dense active suspensions using a generalized hydrodynamic model. Increasing activity induces a structural transition marked by the formation of intense vortices and giant number fluctuations…
We present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a wide class of infinite-dimensional dynamical systems with time-scale separation. The framework is applicable to models where an…
The dynamics of an ensemble of bistable elements under the influence of noise and with global time-delayed coupling is studied numerically by using a Langevin description and analytically by using 1) a Gaussian approximation and 2) a…
We study numerically interaction of spatially localized modes in strongly scattering two-dimensional media. We move eigenvalues in the complex plane by changing gradually the index of a single scatterer. When spatial and spectral overlap is…
Nonlocality is a fundamental concept in photonics. For instance, nonlocal wave-matter interactions in spatially modulated metamaterials enable novel effects, such as giant electromagnetic chirality, artificial magnetism, and negative…
We investigate stationary, spatially localized patterns in lattice dynamical systems that exhibit bistability. The profiles associated with these patterns have a long plateau where the pattern resembles one of the bistable states, while the…
Fundamental solitons pinned to the interface between two discrete lattices coupled at a single site are investigated. Serially and parallel-coupled identical chains (\textit{System 1} and \textit{System 2}), with the self-attractive on-site…
Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that…