Related papers: Analysing transitions from a Turing instability to…
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…
The transition to turbulence via spatiotemporal intermittency is investigated in the context of coupled maps defined on small-world networks. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of…
Active matter systems display a fascinating range of dynamical states, including stationary patterns and turbulent phases. While the former can be tackled with methods from the field of pattern formation, the spatio-temporal disorder of the…
In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing…
Since the pioneering work of Richardson in 1926, later refined by Batchelor and Obukhov in 1950, it is predicted that the rate of separation of pairs of fluid elements in turbulent flows with initial separation at inertial scales, grows…
We study statistical properties of the irregular bursting arising in a class of neuronal models close to the transition from spiking to bursting. Prior to the transition to bursting, the systems in this class develop chaotic attractors,…
We study the local dynamics of $L^{2}\left(\mathbb{R}\right)$-perturbations to the zero solution of spatially $2\pi$-periodic coefficient reaction-diffusion systems. In this case the spectrum of the linearization about the zero solution is…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
The transition to turbulence is characterized by an abrupt loss of order and predictability, featuring the intermittent proliferation and decay of localized turbulent structures. En-route to becoming fully turbulent, surprisingly order…
We consider a class of singularly perturbed 2-component reaction-diffusion equations which admit bistable traveling front solutions, manifesting as sharp, slow-fast-slow, interfaces between stable homogeneous rest states. In many example…
The advection and diffusion of a passive scalar is investigated for a map of the 2-torus. The map is chaotic, and the limit of almost-uniform stretching is considered. This allows an analytic understanding of the transition from a phase of…
Wall-bounded flows experience a transition to turbulence characterized by the coexistence of laminar and turbulent domains in some range of Reynolds number R, the natural control parameter. This transitional regime takes place between an…
We numerically solve the active nematohydrodynamic equations of motion, coupled to a Turing reaction-diffusion model, to study the effect of active nematic flow on the stripe patterns resulting from a Turing instability. If the activity is…
We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…
In this article, we study a system of reaction-diffusion equations in which the diffusivities are widely separated. We report on the discovery of families of spatially periodic canard solutions that emerge from {\em singular Turing…
Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small…
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
We consider turbulence in the Gross-Pitaevsky model and study the creation of a coherent condensate via an inverse cascade originated at small scales. The growth of the condensate leads to a spontaneous breakdown of symmetries of…
We study the coupling induced destabilization in an array of identical oscillators coupled in a ring structure where the number of oscillators in the ring is large. The coupling structure includes different types of interactions with…
The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product networks is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by…