相关论文: Minimal invariant regions and minimal globally att…

Toric differential inclusions occur as key dynamical systems in the context of the Global Attractor Conjecture. We introduce the notions of minimal invariant regions and minimal globally attracting regions for toric differential inclusions.…

We present a mathematical definition for the attainable region of a dynamical system, with primary focus on mass action kinetics for chemical reactions. We characterise this region for linear dynamical systems, and we report on experiments…

We investigate the possibility that for any given reaction rate vector $k$ associated with a network $G$, there exists another network $G'$ with a corresponding reaction rate vector that reproduces the mass-action dynamics generated by…

This paper concerns the long-term behavior of population systems, and in particular of chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two important open problems in the field of Chemical Reaction…

This paper concerns the dynamical behavior of weakly reversible, deterministically modeled population processes near the facets (codimension-one faces) of their invariant manifolds and proves that the facets of such systems are "repelling."…

We discuss the existence of pullback attractors for multivalued dynamical systems on metric spaces. Such attractors are shown to exist without any assumptions in terms of continuity of the solution maps, based only on minimality properties…

We show that weakly reversible mass-action systems can have a continuum of positive steady states, coming from the zeroes of a multivariate polynomial. Moreover, the same is true of systems whose underlying reaction network is reversible…

In the study of reaction networks and the polynomial dynamical systems that they generate, special classes of networks with important properties have been identified. These include reversible, weakly reversible}, and, more recently,…

We construct two examples of invariant manifolds that despite being locally unstable at every point in the transverse direction are globally stable. Using numerical simulations we show that these invariant manifolds temporarily repel nearby…

Invariant manifolds facilitate the understanding of nonlinear stochastic dynamics. When an invariant manifold is represented approximately by a graph for example, the whole stochastic dynamical system may be reduced or restricted to this…

Reaction systems are discrete dynamical systems that model biochemical processes in living cells using finite sets of reactants, inhibitors, and products. We investigate the computational complexity of a comprehensive set of problems…

It is well-known that random attractors of a random dynamical system are generally not unique. We show that for general pullback attractors and weak attractors, there is always a minimal (in the sense of smallest) random attractor which…

This work addresses the problem of estimating the region of attraction (RA) of equilibrium points of nonlinear dynamical systems. The estimates we provide are given by positively invariant sets which are not necessarily defined by level…

Approximating regions of attraction in nonlinear systems require extensive computational and analytical efforts. In this paper, nonlinear vector fields are recasted as sum of vectors where each individual vector is used to construct an…

Persistence and permanence are properties of dynamical systems that describe the long-term behavior of the solutions, and in particular specify whether positive solutions approach the boundary of the positive orthant. Mass-action systems…

We study the dynamics of two bodies moving on elliptic Keplerian orbits around a fixed center of attraction and interacting only by means of elastic or inelastic collisions. We show that there exists a bounded invariant region: for suitable…

We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…

We study general linear transport-reaction systems on an arbitrary dimensional hypercube with periodic boundary conditions. Transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria…

We consider perimeter perturbations of a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. We prove that there exists curves in the…

Receptive field profiles registered by cell recordings have shown that mammalian vision has developed receptive fields tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time.…