Related papers: Spatio-temporal dynamics induced by competing inst…
Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in…
A simple model of wave-particle interaction is studied in its self-consistent form, that is, where the particles are allowed to feedback on the waves dynamics. We focus on the configurations of locked solutions (equilibria) and how the…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
The Whitham equation is a model for the evolution of small-amplitude, unidirectional waves of all wavelengths on shallow water. It has been shown to accurately model the evolution of waves in laboratory experiments. We compute…
We study the nonlinear propagation of electrostatic wave packets in a collisional plasma composed of strongly coupled ions and relativistically degenerate electrons. The equilibrium of ions is maintained by an effective temperature…
The dynamics of the domains is studied in a two-dimensional model of the microphase separation of diblock copolymers in the vicinity of the transition. A criterion for the validity of the mean field theory is derived. It is shown that at…
Polarity fields are known to exhibit long distance patterns, in both physical and biological systems. The mechanisms behind such patterns are poorly understood. Here, we describe the dynamics of polarity fields using an original physical…
In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
In pattern-forming systems, localized patterns are states of intermediate complexity between fully extended ordered patterns and completely irregular patterns. They are formed by stationary fronts enclosing an ordered pattern inside an…
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…
In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show…
In this paper we describe invariant geometrical ~structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact that these states are only marginally…
Focusing on a two-field Swift-Hohenberg model with linear nonreciprocal interactions, this study investigates how emerging higher-codimension points act as organizing centers for the nonequilibrium phase diagram that features various steady…
We study the growth of a periodic pattern in one dimension for a model of spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on the intermediate region, where the non-linearity cannot be negected anymore, and before…
In this paper we present a study of the early stages of unstable state evolution of systems with spatial symmetry changes. In contrast to the early time linear theory of unstable evolution described by Cahn, Hilliard, and Cook, we develop a…
Discrete time evolution of one-dimensional maps is embedded in continuous time by truncating the Taylor series expansion of the time evolution operator to a finite order N. Truncations with N > 4 leads to unconditional instability.…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…