Related papers: Open sub-categorical dynamics in interaction
The main purpose of this paper is to introduce the structure of soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and product. Therefore, the…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances…
It is shown how the macroscopic non-equilibrium dynamics of a class of systems whose microscopic stochastic dynamics involves disordered and frustrated but range-free interactions can be well described by closed deterministic flow…
In the present chapter we study the emergence of global patterns in large groups in first and second-order multi-agent systems, focusing on two ingredients that influence the dynamics: the interaction network and the state space. The state…
To understand galaxies and their evolution, it is necessary to describe how the different scales interact: how the microscopic physics, such as star formation, or the large scale physics, such as galaxy interactions may modify the galaxy…
We introduce a framework that represents a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based only on order-theoretic assumptions and show how applications across almost all…
We investigate global stability and dynamics of large ecological networks by classical methods of the dynamical system theory, including Hamiltonian methods, and averaging. Our analysis exploits the network topological structure, namely,…
In this paper we aim to present two general results regarding, on one hand, the openness stability of set-valued maps and, on the other hand, the metric regularity behavior of the implicit multifunction related to a generalized variational…
In this paper the phenomenon of dynamic heterogeneity in supercooled liquid systems is considered in terms of the recently proposed gauge theory of glass transition. The physical interpretation of the dynamic scaling is considered. It is…
We numerically elucidate the microscopic mechanisms controlling the relaxation dynamics of a three-dimensional lattice glass model that has static properties compatible with the approach to a random first-order transition. At low…
We use a reformulation of compositional game theory to reunite game theory with game semantics, by viewing an open game as the System and its choice of contexts as the Environment. Specifically, the system is jointly controlled by $n \geq…
Complex dynamical networks consisting of many components that interact and produce each other are difficult to understand, especially, when new components may appear. In this paper we outline a theory to deal with such systems. The theory…
Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. So far kinetic constraints have been introduced in idealised models aiming to capture…
In order to investigate collective effects of interactions between pedestrians and attractions, this study extends the social force model. Such interactions lead pedestrians to form stable clusters around attractions, or even to rush into…
Understanding the mechanisms that govern species coexistence and biodiversity represents a fundamental challenge in ecology. This study extends the classic rock-paper-scissors model by introducing a context-dependent higher-order…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
In this paper we extend to a generic class of piecewise smooth dynamical systems a fundamental tool for the analysis of convergence of smooth dynamical systems: contraction theory. We focus on switched systems satisfying Caratheodory…
Global-type formalisms enable to describe the overall behaviour of distributed systems and at the same time to enforce safety properties for communications between system components. Our goal is that of amending a weakness of such…
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…