Related papers: Forward and Pullback Dynamics of Nonautonomous Int…
This work deals with a parametric linear interpolation between an autonomous FitzHugh-Nagumo model and a nonautonomous skewed-problem with the same fundamental structure. This paradigmatic example allows to construct a family of…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
The existence of a pullback attractor is established for the singularly perturbed FitzHugh-Nagumo system defined on the entire space $R^n$ when external terms are unbounded in a phase space. The pullback asymptotic compactness of the system…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
This paper explores a non-linear, non-local model describing the evolution of a single species. We investigate scenarios where the spatial domain is either an arbitrary bounded and open subset of the $n$-dimensional Euclidean space or a…
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator…
This article presents tools for the design of control laws inducing robust controlled forward invariance of a set for hybrid dynamical systems modeled as hybrid inclusions. A set has the robust controlled forward invariance property via a…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
Turbulent flows present rich dynamics originating from non-trivial energy fluxes across scales, non-stationary forcings and geometrical constraints. This complexity manifests in non-hyperbolic chaos, randomness, state-dependent persistence…
In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide…
Non-conformal attractor behavior is studied by solving non-conformal second order viscous hydrodynamics with respect to boost-invariant plasmas. Numerical solutions of the relative decay rate of the enthalpy density, the inverse shear and…
Direct design of a robot's rendered dynamics, such as in impedance control, is now a well-established control mode in uncertain environments. When the physical interaction port variables are not measured directly, dynamic and kinematic…
The paper extends well-posedness results of a previously explored class of time-shift invariant evolutionary problems to the case of non-autonomous media. The Hilbert space setting developed for the time-shift invariant case can be utilized…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
Artificial ecosystems provide an additional experimental tool to support laboratory work, field work, and theoretical development in competitive exclusion research. A novel application of a spatiotemporal agent based model is presented…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
As it is well-known, the forwards and pullback dynamics are in general unrelated. In this paper we present an in-depth study of whether the pullback attractor is also a forwards attractor for the processes involved with the skew-product…
This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of…
Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality…