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We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We…
Doubly diffusive convection is considered in a vertical slot where horizontal temperature and solutal variations provide competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, the…
We investigate a two-component reaction-diffusion system with a slow-fast structure and spatially varying coefficients $f_1$ and $f_2$ appearing in the slow equation. Under mild boundedness and regularity conditions on $f_1$ and $f_2$ the…
We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are…
The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
A tube conveying a large amount of fluid with a free outlet does not sit still. We construct and analyze a nonlinear evolution equation describing such phenomena. Two types of boundary conditions at the inlet are considered, one for which…
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
Although the roll/streak structure is ubiquitous in pre-transitional wall-bounded shear flow, this structure is linearly stable if the idealization of laminar flow is made. Lacking an instability, the large transient growth of the…
We study the structure of stationary non equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non…
Chemical, physical and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semi-stable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with…
In this paper, we analyse the dynamics of a pattern-forming system close to simultaneous Turing and Turing--Hopf instabilities, which have a 1:1 spatial resonance, that is, they have the same critical wave number. For this, we consider a…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
Fast-slow systems are studied usually by "geometrical dissection". The fast dynamics exhibit attractors which may bifurcate under the influence of the slow dynamics which is seen as a parameter of the fast dynamics. A generic solution comes…
The effect of thermally generated bulk stochastic forces on the statistical growth dynamics of forwards bifurcating propagating macroscopic patterns is compared with the influence of fluctuations at the boundary of a semiinfinite system,…
In this paper, we study a class of equations representing nonlinear diffusion on networks. A particular instance of our model can be seen as a network equivalent of the porous-medium equation. We are interested in studying perturbations of…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a non-equilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation…