Related papers: Unstable dimension variability and synchronization…
In this work we discuss the most recent results concerning the Vlasov dynamics inside the spinodal region. The chaotic behaviour which follows an initial regular evolution is characterized through the calculation of the fractal dimension of…
Recent research on the dynamics of certain fluid dynamical instabilities shows that when there is a slow invariant manifold subject to fast timescale instability the dynamics are extremely sensitive to noise. The behaviour of such systems…
A multi-dimensional switched system or multi-mode multi-dimensional ($M^3D$) system extends the classic switched system by allowing different subsystem dimensions. The stability problem of the $M^3D$ system, whose state transitions at…
Random neural networks are dynamical descriptions of randomly interconnected neural units. These show a phase transition to chaos as a disorder parameter is increased. The microscopic mechanisms underlying this phase transition are unknown,…
Instabilities of equilibrium quantum mechanics are common and well-understood. They are manifested for example in phase transitions, where a quantum system becomes so sensitive to perturbations that a symmetry can be spontaneously broken.…
Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-B\'enard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov…
We present the results of a wavelet-based approach to the study of the chaotic dynamics of a one dimensional model that shows a direct transition to spatiotemporal chaos. We find that the dynamics of this model in the spatiotemporally…
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 study two-dimensional chaotic standard maps coupled along the edges of scale-free trees and tree-like subgraph (4-star) with a non-symplectic coupling and time delay between the nodes. Apart from the chaotic and regular 2-periodic…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…
Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…
The dynamics of coupled 2D chaotic maps with time-delay on a scalefree-tree is studied, with different types of the collective behaviors already been reported for various values of coupling strength [1]. In this work we focus on the…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
Adaptive controllers are designed to synchronize two different chaotic systems with uncertainties, including unknown parameters, internal and external perturbations. Lyapunov stability theory is applied to prove that under some conditions…
The linear stability of a shear-thinning, viscoelastic fluid undergoing any of the canonical rectilinear shear flows, viz., plane Couette flow and pressure-driven flow through a channel or a tube is analyzed in the creeping-flow limit using…
An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential…
An analysis of transition from chaotic to nonchaotic behavior and synchronization in an ensemble of systems driven by identical random forces is presented. The synchronization phenomenon is investigated in the ensemble of particles moving…
We discuss chaotic advection in three-dimensional unsteady incompressible laminar flow, and analyse in detail the most important novel advection phenomenon in these flows; the global dispersion of passive scalars in flows with two slow and…
Empirical diagnosis of stability has received considerable attention, mostly focused on variance metrics for early warning signals of abrupt system change. Despite this, the theoretical foundation and application has been limited to…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…