Related papers: Piecewise linear cusp bifurcations in ultradiscret…
This work analyzes fractional continuous-time random walks on two-layer multiplexes. A node-centric dynamics is used, in which it is assumed a Poisson distribution of a walker to become active, while a jump to one of its neighbors depends…
We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological…
Driven quantum systems coupled to an environment typically exhibit effectively thermal behavior with relaxational dynamics near criticality. However, a different qualitative behavior might be expected in the weakly dissipative limit due to…
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,…
Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The…
The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have real rational number values. Applicable characteristic…
This paper presents a mathematical model for the train dynamics in a mass-transit metro line system with one symmetrically operated junction. We distinguish three parts: a central part and two branches. The tracks are spatially discretized…
This work proposes an accelerated primal-dual dynamical system for affine constrained convex optimization and presents a class of primal-dual methods with nonergodic convergence rates. In continuous level, exponential decay of a novel…
We study the distribution of the sequence of elements of the discrete dynamical system generated by the M\"obius transformation $x \mapsto (ax + b)/(cx + d)$ over a finite field of $p$ elements. Motivated by a recent conjecture of P.…
We rigorously show that a class of systems of partial differential equations modeling wave bifurcations supports stationary equivariant bifurcation dynamics through deriving its full dynamics on the center manifold(s). A direct consequence…
We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple…
In this work we establish that finite directed graphs give rise to semiflows on the power set of their nodes. We analyze the topological dynamics for semiflows on finite directed graphs by characterizing Morse decompositions, recurrence…
Representation of nonlinear dynamical systems as infinite-dimensional linear operators over Hilbert spaces enables analysis of nonlinear systems via pseudo-spectral operator analysis. In this paper, we provide a novel representation for…
We study the complex nonlinear dynamics of the two-photon Dicke model in the semiclassical limit by considering cavity and qubit dissipation. In addition to the normal and super-radiant phases, another phase that contains abundant…
We compute the dynamical degrees of certain compositions of reflections in points on a smooth cubic fourfold. Our interest in these computations stems from the irrationality problem for cubic fourfolds. Namely, we hope that they will…
The subject of the work are pairs of linearly coupled PT-symmetric dimers. Two different settings are introduced, namely, straight-coupled dimers, where each gain site is linearly coupled to one gain and one loss site, and cross-coupled…
We describe a method to analyze and decompose the dynamics of a control system on a Lie group subject to symmetries. The method is based on the concept of generalized Young symmetrizers of representation theory. It naturally applies to the…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
In this work, we illustrate the underlying mathematical structure of mixed-dimensional models arising from the composition of graphs and continuous domains. Such models are becoming popular in applications, in particular, to model the human…
We investigate piecewise deterministic Markov processes (PDMP), where the deterministic dynamics follows a scalar conservation law and random jumps in the system are characterized by changes in the flux function. We show under which…