Related papers: Intermediate physical interactions induce spatiote…
In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability…
In this article we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
Turbulence, namely, irregular fluctuations in space and time characterize fluid flows in general and atmospheric flows in particular.The irregular,i.e., nonlinear space-time fluctuations on all scales contribute to the unpredictable nature…
When an ensemble of particles interact hydrodynamically, they generically display large-scale transient structures such as swirls in sedimenting particles [1], or colloidal strings in sheared suspensions [2]. Understanding these…
In most systems, its division into interacting constituent elements gives rise to a natural network structure. Analyzing the dynamics of these elements and the topology of these natural graphs gave rise to the fields of (nonlinear) dynamics…
Front dynamics modeled by a reaction-diffusion equation are studied under the influence of spatio-temporal structured noises. An effective deterministic model is analytical derived where the noise parameters, intensity, correlation time and…
Nonreciprocal interactions that violate Newton's law 'actio=reactio' are ubiquitous in nature and are currently intensively investigated in active matter, chemical reaction networks, population dynamics, and many other fields. An…
We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Non equilibrium structures are shown to correspond to statistical…
We investigate how momentum and kinetic energy is transferred between Fourier components (the so-called triad interactions) in measured turbulent flow fields, i.e. in practical, discretely sampled signals with limited temporal and spatial…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
In this paper we give a general account of Wave Interaction Theory which by now consists of two parts: kinetic wave turbulence theory (WTT), using a statistical description of wave interactions, and the D-model recently introduced in…
Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of…
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…
The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and…
Bacteria possess diverse mechanisms to regulate their motility in response to environmental and physiological signals, enabling them to navigate complex habitats and adapt their behavior. Among these mechanisms, interspecies recognition…
The universal equations describing collective oscillations of the multidomain patterns of small period in an arbitrary $d$-dimensional reaction-diffusion system of the activator-inhibitor type are asymptotically derived. It is shown that…
Chemically active mixtures exhibit complex patterns that emerge from the interplay of physical interactions and reactions among components. Individually, these two processes are well-understood: Physical interactions can give rise to phase…
Interference patterns associated with soliton-soliton interaction are investigated in detail. We find that the temporal and spatial interference patterns exhibit quite different characteristics. The period of the spatial interference…