相关论文: Existence of Unpredictable Solutions and Chaos
We consider here a recently proposed geometrical criterion for local instability based on the geodesic deviation equation. Although such a criterion can be useful in some cases, we show here that, in general, it is neither necessary nor…
The infinite-dimensional mechanics of fluids and plasmas can be formulated as "noncanonical" Hamiltonian systems on a phase space of Eulerian variables. Singularities of the Poisson bracket operator produce singular Casimir elements that…
The paper discusses the main ideas of the chaos theory and presents mainly the importance of the nonlinearities in the mathematical models. Chaos and order are apparently two opposite terms. The fact that in chaos can be found a certain…
This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general…
The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
This is a survey on the recent theory of chaos in partial differential equations.
We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…
In a recent Letter [PRL 101, 074101 (2008)], Kapulkin and Pattanayak presented evidence that a quantum Duffing oscillator, sufficiently damped so that it is not classically chaotic, becomes chaotic in the transition region between quantum…
This paper shows that with mechanistic primary budget rules and with some simple assumptions on interest rates the well-known debt dynamics equation transforms into the infamous logistic map. The logistic map has very peculiar and rich…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise…
Admissible perturbations (i.e., perturbations that do not change the Mironenko reflecting function of the system) are obtained for an autonomous three-dimensional quadratic generalized Langford system with five parameters. The obtained…
We use Lyapunov-like functions and convex optimization to propagate uncertainty in the initial condition of nonlinear systems governed by ordinary differential equations. We consider the full nonlinear dynamics without approximation,…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
\textit{Non-statistical dynamics} are those for which a set of points with positive measure (w.r.t. a reference probability measure which is in most examples the Lebesgue on a manifold) do not have a convergent sequence of empirical…
This note provides a general construction, and gives a concrete example of, forced ordinary differential equation systems that have these two properties: (a) for each constant input u, all solutions converge to a steady state but (b) for…
In this paper, we discuss the relationships between stability and almost periodicity for solutions of stochastic differential equations. Our essential idea is to get stability of solutions or systems by some inherited properties of Lyapunov…
The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain non-periodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in…