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Gradual advancement of control technology gives rise to the studies of the stability of linear systems. The stability of the linear multiagent system is motivated by increasing utilization of agent dynamics together with the number of…
We consider a novel model of stochastic replicator dynamics for potential games that converts to a Langevin equation on a sphere after a change of variables. This is distinct from the models studied earlier. In particular, it is ill-posed…
While the statics of many simple physical systems reproduce the striking number-theoretical patterns found in the phyllotaxis of living beings, their dynamics reveal unusual excitations: multiple classical rotons and a large family of…
In the stability theory of dynamical systems, Lyapunov functions play a fundamental role. In this paper, we study the attractor-repeller pair decomposition and Morse decomposition for compact metric space in the random setting. In contrast…
We formulate a dynamical system based on many-index objects. These objects yield a generalization of the Heisenberg's equation. Systems describing harmonic oscillators are given.
The article is devoted to the issues of using discrete simulation models for modeling some basic technological processes. In the scientific work, models in the form of multi-agent systems have been investigated, which allow us to consider a…
In a previous work we considered a two-dimensional lattice of particles and calculated its time evolution by using an interaction law based on the spatial position of the particles themselves. The model reproduced the behaviour of…
Biological networks of interacting agents exhibit similar topological properties for a wide range of scales, from cellular to ecological levels, suggesting the existence of a common evolutionary origin. A general evolutionary mechanism…
People tend to align their use of language to the linguistic behaviour of their own ingroup and to simultaneously diverge from the language use of outgroups. This paper proposes to model this phenomenon of sociolinguistic identity…
Lyapunov exponents are indicators for the chaotic properties of a classical dynamical system. They are most naturally defined in terms of the time evolution of a set of so-called covariant vectors, co-moving with the linearized flow in…
Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…
In this paper, a distributed optimization problem with general differentiable convex objective functions is studied for single-integrator and double-integrator multi-agent systems. Two distributed adaptive optimization algorithm is…
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of…
The quality of a simulator equipped with a haptic interface is given by the dynamical properties of its components: haptic interface, simulator and control system. Some application areas of such kind of simulator like musical synthesis,…
The notion of Lyapunov function plays a key role in design and verification of dynamical systems, as well as hybrid and cyber-physical systems. In this paper, to analyze the asymptotic stability of a dynamical system, we generalize standard…
The notion of feedback integrators permits Euclidean integration schemes for dynamical systems evolving on manifolds. Here, a constructive Lyapunov function for the attitude dynamics embedded in an ambient Euclidean space has been proposed.…
Proper states' representations are the key to the successful dynamics modeling of chaotic systems. Inspired by recent advances of deep representations in various areas such as natural language processing and computer vision, we propose the…
Many complex systems can be modeled as multiagent systems in which the constituent entities (agents) interact with each other. The global dynamics of such a system is determined by the nature of the local interactions among the agents.…
A general framework of evolutionary dynamics under heterogeneous populations is presented. The framework allows continuously many types of heterogeneous agents, heterogeneity both in payoff functions and in revision protocols and the entire…