Related papers: Numerical Dynamics of Integrodifference Equations:…
The derivation of a Moving Boundary Approximation or of the response of a coherent structure like a front, vortex or pulse to external forces and noise, is generally valid under two conditions: the existence of a separation of time scales…
Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor. This paper provides characterizations of attractors for the wider class of coherent systems, defined by…
If the semigroup is slowly non-dissipative, i.e., its solutions can diverge to infinity as time tends to infinity, one still can study its dynamics via the approach by the unbounded attractors - the counterpart of the classical notion of…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
In this paper, tools to study forward invariance properties with robustness to dis- turbances, referred to as robust forward invariance, are proposed for hybrid dynamical systems modeled as hybrid inclusions. Hybrid inclusions are given in…
A coupled computational approach to simultaneously learn a vector field and the region of attraction of an equilibrium point from generated trajectories of the system is proposed. The nonlinear identification leverages the local stability…
The initial boundary value problem for a nonlinear system of equations modeling the chevron patterns is studied in one and two spatial dimensions. The existence of an exponential attractor and the stabilization of the zero steady state…
We develop a general compactification framework to facilitate analysis of nonlinear nonautonomous ODEs where nonautonomous terms decay asymptotically. The strategy is to compactify the problem: the phase space is augmented with a bounded…
A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie…
We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit…
We consider SDEs driven by two different sources of additive noise, which we refer to as intrinsic and common. We establish almost sure existence and uniqueness of pullback attractors with respect to realisations of the common noise only.…
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
For autonomous Lotka-Volterra systems of differential equations modelling the dynamics of n competing species, new criteria are established for the existence of a single point global attractor. Under the conditions of these criteria, some…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding modes. If one uses one of the well-known…
Regularity properties of the pressure are related to phase transitions. In this article we study thermodynamic formalism for systems defined in non-compact phase spaces, our main focus being countable Markov shifts. We produce metric…
We apply the dynamical approach to the study of the second order semi-linear elliptic boundary value problem in a cylindrical domain with a small parameter at the second derivative with respect to the "time" variable corresponding to the…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
We examine "dynamical similarities" in the Lagrangian framework. These are symmetries of an intrinsically determined physical system under which observables remain unaffected, but the extraneous information is changed. We establish three…
We compare the dimension of a non-invertible self-affine set to the dimension of the respective invertible self-affine set. In particular, for generic planar self-affine sets, we show that the dimensions coincide when they are large and…