Related papers: Weakly nonlinear analysis in spatially extended sy…
We consider a class of dynamical systems, which we call weakly coarse expanding, which is a generalization to the postcritically infinite case of expanding Thurston maps as discussed by Bonk-Meyer and is closely related to coarse expanding…
We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe…
It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the…
A stability analysis is made for a non-singular pre-big-bang like cosmological model based on 1-loop corrected string effective action. Its homogeneous and isotropic solution realizes non-singular transition from de Sitter universe to…
In recent years, a new method for experimental nonlinear modal analysis has been developed, which is based on the extended periodic motion concept. The method is well suited to experimentally obtain amplitude-dependent modal properties…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
We present the applications of methods from nonlinear local harmonic analysis for calculations in nonlinear collective dynamics described by different forms of Vlasov-Maxwell-Poisson equations. Our approach is based on methods provided the…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…
We consider random perturbations of discrete-time dynamical systems. We give sufficient conditions for the stochastic stability of certain classes of maps, in a strong sense. This improves the main result in J. F. Alves, V. Araujo, Random…
We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under smooth perturbations. On one hand we…
High-dimensional systems that have a low-dimensional dominant behavior allow for model reduction and simplified analysis. We use differential analysis to formalize this important concept in a nonlinear setting. We show that dominance can be…
This paper formalises the concepts of weakly and weakly regularly persistent input trajectory as well as their link to the Observability Grammian and the existence and uniqueness of solutions of Moving Horizon Estimation (MHE) problems.…
This paper presents our ongoing work on spatio-temporal models for formal analysis and property-based testing. Our proposed framework aims at reducing the impedance mismatch between formal methods and practitioners. We introduce a set of…
The Discrete Nonlinear Schroedinger Equation with a random potential in one dimension is studied as a dynamical system. It is characterized by the length, the strength of the random potential and by the field density that determines the…
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
It is known that the Swift-Hohenberg equation $\partial u/\partial t = -(\partial_x^2 + 1)^2u + \varepsilon (u-u^3)$ can be reduced to the Ginzburg-Landau equation (amplitude equation) $\partial A/\partial t = 4\partial_x^2 A + \varepsilon…
For a general discrete dynamics on a Banach and Hilbert spaces we give necessary and sufficient conditions of the existence of bounded solutions under assumption that the homogeneous difference equation admits an discrete dichotomy on the…
Nonlinear dynamical systems possessing reflection symmetry have an invariant subspace in the phase space. The dynamics within the invariant subspace can be random or chaotic. As a system parameter changes, the motion transverse to the…