Related papers: A multi-dimensional-time dynamical system
Given a dynamical system, we study the so-called space of shift functions thus introducing another vision on bifurcations and chaos. As an application of the obtained results, we give a partial solution to an open problem formulated in…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
The multidimensional ($n$-D) systems described by Roesser model are presented in this paper. These $n$-D systems consist of discrete systems and continuous fractional order systems with fractional order $\nu$, $0<\nu<1$. The stability and…
We develop a principled mathematical framework for controlling nonlinear, networked dynamical systems. Our method integrates dimensionality reduction, bifurcation theory and emerging model discovery tools to find low-dimensional subspaces…
A sequential dynamical system (SDS) consists of a graph, a set of local functions and an update schedule. A linear sequential dynamical system is an SDS whose local functions are linear. In this paper, we derive an explicit closed formula…
Dynamical systems---by which we mean machines that take time-varying input, change their state, and produce output---can be wired together to form more complex systems. Previous work has shown how to allow collections of machines to…
This paper deals with the Vlasov-Stokes' system in three dimensions with periodic boundary conditions in the spatial variable. We prove the existence of a unique strong solution to this two-phase model under the assumption that initial…
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete…
Periodic control systems used in spacecrafts and automotives are usually period-driven and can be decomposed into different modes with each mode representing a system state observed from outside. Such systems may also involve intensive…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
The intermediate dynamics of composed one-dimensional maps is used to multiply attractors in phase space and create multiple independent bifurcation diagrams which can split apart. Results are shown for the composition of k-paradigmatic…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
In this paper we analyze the flow of a family of three dimensional Lotka-Volterra systems restricted to an invariant and bounded region. The behaviour of the flow in the interior of this region is simple: either every orbit is a periodic…
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…
Research on long-term time series prediction has primarily relied on Transformer and MLP models, while the potential of convolutional networks in this domain remains underexplored. To address this, we propose a novel multi-scale time series…
We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…
We present a mathematical model: dynamical systems over finite sets (DSF), and we show that Boolean and discrete genetic models are special cases of DFS. In this paper, we prove that a function defined over finite sets with different number…
We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…
We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…