Related papers: Invariant Manifolds of Complex Systems
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Our aim in this paper is to establish stable manifolds near hyperbolic equilibria of fractional differential equations in arbitrary finite dimensional spaces.
We present and implement an algorithm for computing the invariant circle and the corresponding stable manifolds for 2-dimensional maps. The algorithm is based on the parameterization method, and it is backed up by an a-posteriori theorem…
We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…
We classify invariant curves for birational surface maps that are expanding on cohomology. When the expansion is exponential, the arithmetic genus of an invariant curve is at most one. This implies severe constraints on both the type and…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
We consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flow represents the evolution of a two--dimensional…
Automated program verification often proceeds by exhibiting inductive invariants entailing the desired properties.For numerical properties, a classical class of invariants is convex polyhedra: solution sets of system of linear…
Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of networks based on recurrences in phase space…
This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the…
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
Integrodifference equations are versatile models in theoretical ecology for the spatial dispersal of species evolving in non-overlapping generations. The dynamics of these infinite-dimensional discrete dynamical systems is often illustrated…
We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The problem of reduced description is studied as a problem of constructing the slow…
We investigate the topological properties of invariant sets associated with the dynamics of scattering systems with three or more degrees of freedom. We show that the asymptotic separation of one degree of freedom from the rest in the…
Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…
We use the version of the Lyapunov--Perron method operating on individual solutions to investigate the existence of invariant manifolds for non-autonomous dynamical systems, focusing in particular on inertial and stable manifolds. We…
In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain diverse tangency points. We show that the slow divergence…
Dynamical-systems approaches to spatiotemporal chaos have been developed primarily for single-phase flows, where the system state is defined by bulk velocity fields. Extending these ideas to two-phase flows remains challenging because the…