Related papers: Finite dynamical systems, hat games, and coding th…
We revisit the complexity of the well-studied notion of Additively Separable Hedonic Games (ASHGs). Such games model a basic clustering or coalition formation scenario in which selfish agents are represented by the vertices of an…
Hypergraphs naturally represent higher-order interactions, which persistently appear from social interactions to neural networks and other natural systems. Although their importance is well recognized, a theoretical framework to describe…
A `symbolic dynamical system' is a continuous transformation F:X-->X of a closed perfect subset X of A^V, where A is a finite set and V is countable. (Examples include subshifts, odometers, cellular automata, and automaton networks.) The…
Static and dynamic equilibria in noisy binary choice (Ising) games on complete and random graphs in the annealed approximation are analysed. Two versions, an Ising game with interaction term defined in accordance with the Ising model in…
In this paper, we extend the notion of finite-time input-to-state stability (FTISS) for finite-dimensional systems to infinite-dimensional systems. More specifically, we first prove an FTISS Lyapunov theorem for a class of…
In this paper implicit and explicit exact difference schemes (EDS) for system $\textbf{x}' = A\textbf{x}$ of three linear differential equations with constant coefficients are constructed. Numerical simulations for stiff problem and for…
This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…
The dynamics and stability of multi-spot patterns to the Gray-Scott (GS) reaction-diffusion model in a two-dimensional domain is studied in the singularly perturbed limit of small diffusivity $\epsilon$ of one of the two solution…
When neural networks are trained from data to simulate the dynamics of physical systems, they encounter a persistent challenge: the long-time dynamics they produce are often unphysical or unstable. We analyze the origin of such…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
The guessing number of a directed graph (digraph), equivalent to the entropy of that digraph, was introduced as a direct criterion on the solvability of a network coding instance. This paper makes two contributions on the guessing number.…
We study the dynamics of bond-disordered Ising spin systems on random graphs with finite connectivity, using generating functional analysis. Rather than disorder-averaged correlation and response functions (as for fully connected systems),…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
Deep learning systems achieve remarkable empirical performance, yet the stability of the training process itself remains poorly understood. Training unfolds as a high-dimensional dynamical system in which small perturbations to…
Diffusion and flow-driven instability, or transport-driven instability, is one of the central mechanisms to generate inhomogeneous gradient of concentrations in spatially distributed chemical systems. However, verifying the transport-driven…
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
We study the linear stability of holographic homogeneous solids (HHS) at finite temperature and in presence of a background shear strain by means of a large scale quasi-normal mode analysis which extends beyond the hydrodynamic limit. We…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…