Related papers: Synchronizing Dynamical Systems: their groupoids a…
We characterize synchronization phenomenon in discrete-time, discrete-state random dynamical systems, with random and probabilistic Boolean networks as particular examples. In terms of multiplicative ergodic properties of the induced linear…
Developments in dynamical systems theory provides new support for the discretisation of \pde{}s and other microscale systems. By systematically resolving subgrid microscale dynamics the new approach constructs asymptotically accurate,…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
Spatially extended dynamical systems, namely coupled map lattices, driven by additive spatio-temporal noise are shown to exhibit stochastic synchronization. In analogy with low-dymensional systems, synchronization can be achieved only if…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
We study general random dynamical systems of continuous maps on some compact metric space. Assuming a local contraction condition and uniqueness of the stationary measure, we establish probabilistic limit laws such as the central limit…
We discuss the variety of coordinates often used to characterize the coherent state classical limit of an algebraic model. We show selection of appropriate coordinates naturally motivates a procedure to generate a single particle…
Symmetric hyperbolic systems of equations are explicitly constructed for a general class of tensor fields by considering their structure as r-fold forms. The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance of the…
We study the dynamics of condensation of the inclusion process on a one-dimensional periodic lattice in the thermodynamic limit, generalising recent results on finite lattices for symmetric dynamics. Our main focus is on totally asymmetric…
Full synchronization of dynamical elements coupled via hypergraphs can be analyzed with the hypergraph projection onto dyadic matrices, but this is not sufficient for analyzing cluster synchronization. Here we develop the necessary…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…
We consider synchronization of coupled dynamical systems when different types of interactions are simultaneously present. We assume that a set of dynamical systems are coupled through the connections of two or more distinct networks (each…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
We have introduced a notion of $C^*$-symbolic dynamical system in [K. Matsumoto: Actions of symbolic dynamical systems on $C^*$-algebras, to appear in J. Reine Angew. Math.], that is a finite family of endomorphisms of a $C^*$-algebra with…
We study synchronisation between periodically driven, interacting classical spins undergoing a Hamiltonian dynamics. In the thermodynamic limit there is a transition between a regime where all the spins oscillate synchronously for an…
This paper surveys the recent advances in the interactions between symbolic dynamics and C*-algebras. We explain how conjugacies and orbit equivalences of both two-sided (invertible) and one-sided (noninvertible) symbolic systems may be…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
C*-bundle dynamical systems are introduced and their r\^ole within the theory of C*-subalgebras and Fell bundles is investigated. A C*-bundle dynamical system involves an action of a 1-parameter group of "spatial automorphisms" of the…
The main focus of this paper is to explore how much similarity between two stochastic differential systems. Motivated by the conjugate theory of stochastic dynamic systems, we study the relationship between two systems by finding…