Related papers: Analysis and Characterization of Complex Spatio-te…
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…
The stationary-state spatial structure of reacting scalar fields, chaotically advected by a two-dimensional large-scale flow, is examined for the case for which the reaction equations contain delay terms. Previous theoretical investigations…
We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a…
We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction $A + B \to S$ in a vertical Hele-Shaw cell under constant gravity. We have recently reported that concentration-dependent…
The spatiotemporal dynamics of Lyapunov vectors (LVs) in spatially extended chaotic systems is studied by means of coupled-map lattices. We determine intrinsic length scales and spatiotemporal correlations of LVs corresponding to the…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
Complex spatiotemporal dynamics have been a subject of recent experimental investigations in optical frequency comb microresonators and in driven fiber cavities with a Kerr-type media. We show that this complex behavior has a spatiotemporal…
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…
The processes in nonequilibrium dissipative media caused by coherent structure formation and lead to the complicated dynamics are of interest for nonlinear physics. Here we consider a model of the flow of interacting electronics patterns.…
We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…
We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
We study spatio-temporal bursting in a three-scale reaction diffusion equation organized by the winged cusp singularity. For large time-scale separation the model exhibits traveling bursts, whereas for large space-scale separation the model…
We present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic { theory} model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
We study the spatial patterns formed by interacting biological populations or reacting chemicals under the influence of chaotic flows. Multiple species and nonlinear interactions are explicitly considered, as well as cases of smooth and…
The replicator equation is ubiquitous for many areas of mathematical biology. One of major shortcomings of this equation is that it does not allow for an explicit spatial structure. Here we review analytical approaches to include spatial…
Spatiotemporal pattern formations in two-layer coupled reaction-diffusion Lengyel-Epstein system with distributed delayed couplings are investigated. Firstly, for the original decoupled system, it is proved that when the intra-reactor…
In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the…
We consider reaction-diffusion systems and other related dissipative systems on unbounded domains which would have a Liapunov function (and gradient structure) when posed on a finite domain. In this situation, the system may reach local…