Related papers: A Lax Functorial Definition of Open Dynamics
A system of $N$ interacting objects with internal degrees of freedom is considered. Derivation of system of equations for the description of two interacting objects with spin is given. Relations between the parameters describing subsystems…
We descibe a number of dynamical systems that are generalizations of S. Kowalevskaya system and admit the Lax representation.
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…
Categorical semantics of type theories are often characterized as structure-preserving functors. This is because in category theory both the syntax and the domain of interpretation are uniformly treated as structured categories, so that we…
Several notions of "analytic" functor introduced recently in the literature fit into the graphic fourier transform context presented in [D].
We propose a unified definition for synchronization. By example we show that the synchronization phenomena discussed in the dynamical systems literature can be described within the framework of this definition.
The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function $f$, not of variables, having a…
We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift…
We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph…
It is shown that the mixed states of a closed dynamics support a reduplicated symmetry, which is reduced back to the subgroup of the original symmetry group when the dynamics is open. The elementary components of the open dynamics are…
The paper argues that attracting more economists and adopting a more-precise definition of dynamic complexity might help econophysics acquire more attention in the economics community and bring new lymph to economic research. It may be…
This article is a short introduction to Combinatorial Dynamics for topologists.
Rewriting systems are often defined as binary relations over a given set of objects. This simple definition is used to describe various properties of rewriting such as termination, confluence, normal forms etc. In this paper, we introduce a…
Topological dynamical systems $(X,T)$ are actions $T \times X \to X$, given as $(t, x) \to tx$, on a compact, Hausdorff topological space $X$ with $T$ as an acting group or monoid. We take up the property of topological transitivity…
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…
We define the notion of linguistic structure on a small category, in order to provide a more formal description of ontology logs, also known as ologs, introduced by R. E. Kent and D. I. Spivak in their paper "Ologs: A categorical framework…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…
In recently introduced schematic lattice gas models for vibrated dry granular media, we study the dynamical response of the system to small perturbations of shaking amplitudes and its relations with the characteristic fluctuations. Strong…
The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.