Related papers: On multistability behavior of Unstable Dissipative…
Two coupled, interpenetrating fluids suffer instabilities beyond certain critical counterflows. For ideal fluids, an energetic instability occurs at the point where a sound mode inverts its direction due to the counterflow, while dynamical…
The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the…
Periodic travelling waves (PTW) are a common solution type of partial differential equations. Such models exhibit multistability of PTWs, typically visualised through the Busse balloon, and parameter changes typically lead to a cascade of…
This paper deals with classes of (de)stabilizing switching signals for switched systems. Most of the available conditions for stability of switched systems are sufficient in nature, and consequently, their violation does not conclude…
Nonreciprocal coupling can alter the transport properties of material media, producing striking phenomena such as unidirectional amplification of waves, boundary modes, or self-assembled pattern formation. It is responsible for nonlinear…
In this paper, we consider a planar dynamical system with a piecewise linear function containing an arbitrary number (but finite) of dropping sections and approximating some continuous nonlinear function. Studying all possible local and…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…
We consider a dynamical system in R driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Levy noise of small intensity and such that the heaviest tail…
Elliptical instability is due to a parametric resonance of two inertial modes in a fluid velocity field with elliptical streamlines. This flow is a simple model of the motion in a tidally deformed, rotating body. Elliptical instability…
The neural dynamics of the nematode C. elegans are experimentally low-dimensional and correspond to discrete behavioral states, where previous modeling work has found neural proxies for some of these states. Experimental results further…
For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we find that there is an ensemble of unstable periodic orbits (UPOs) with the special property that the expectation values of macroscopic quantities…
In a recent letter [Phys.Rev.Lett. {\bf 30}, 3269 (1995), chao-dyn/9510011], we reported that a macroscopic chaotic determinism emerges in a multistable system: the unidirectional motion of a dissipative particle subject to an apparently…
Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…
An aspect of the synchronization dynamics is investigated in this work. We argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits unstable dimension variability. Unstable dimension…
We study dynamics of a bimodal planar linear switched system with a Hurwitz stable and an unstable subsystem. For given \textit{flee time} from the unstable subsystem, the goal is to find corresponding \textit{dwell time} in the Hurwitz…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…
We discuss an open driven-dissipative many-body system, in which the competition of unitary Hamiltonian and dissipative Liouvillian dynamics leads to a nonequilibrium phase transition. It shares features of a quantum phase transition in…
This paper provides sufficient conditions for stability of switched linear systems under dwell-time switching. Piece-wise quadratic functions are utilized to characterize the Lyapunov functions and bilinear matrix inequalities conditions…
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…