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The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
In this paper, we introduce a new class of dynamical systems on a coarse space with coarse time called, coarse dynamical system. The notion of coarse conjugacy is studied from coarse geometry point of view. Coarse orbits as invariant sets…
Dynamical Systems is a field that studies the collective behavior of objects that update their states according to some rules. Discrete-time Boolean Finite Dynamical System (DT-BFDS) is a subfield where the systems have some finite number…
Quantum droplets are ultradilute liquid states which emerge from the competitive interplay of two Hamiltonian terms, the mean-field energy and beyond-mean-field correction, in a weakly interacting binary Bose gas. We relate the formation of…
We review a (constructive) approach first introduced in [6] and further developed in [7, 8, 38, 9] for hydrodynamic limits of asymmetric attractive particle systems, in a weak or in a strong (that is, almost sure) sense, in an homogeneous…
Cavitation is a general phenomenon of the fluid flows with obstacles. It appears in the cooling conduits of the fast nuclear engines. A model of this phenomenon using the theory of Laplace and a common non-convex energy for the liquid and…
Stokesian Dynamics is a well-established computational method for simulating dynamics of many particles suspended in a conventional passive fluid medium. Active fluids composed of self-propelling particles with broken time reversal symmetry…
A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to…
A manifestly covariant equation is derived to describe the perturbations in a domain wall on a given background spacetime. This generalizes recent work on domain walls in Minkowski space and introduces a framework for examining the…
We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of…
This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…
A new kinetic model of globular clusters based on a modified velocities distribution function is compared to the most often used King's model. A hypothetical contribution of dark matter is considered.
This paper studies a new and more general axiomatization than one presented previously for preference on likelihood gambles. Likelihood gambles describe actions in a situation where a decision maker knows multiple probabilistic models and a…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…