We analyse the chaotic motion of a periodically driven damped pendulum. Time series of the angular velocity are sampled and investigated numerically. Parameters of the driving force and the damping are reconstructed from the velocity by numerically adapting the equation of motion. The delay time required to embed the attractor in a space of delay coordinates is derived from an extension of the ...

Invariant sets embedded in a chaotic attractor can generate time averages that diier from the average generated by typical orbits on the attractor. Motivated by two diierent topics (namely, controlling chaos and riddled basins of attraction), we consider the question of which invariant set yields the largest (optimal) value of an average of a given smooth function of the system state. We presen...

25 On the genetic "memory" of chaotic attractor of the barotropic ocean model. Abstract. The structure of the attractor of the barotropic ocean model is studied in this paper. This structure is partially explained by the sequence of bifurcation the system is subjected by variations of the leading parameters. The principal feature of the studied system is the existence of two "almost invariant" ...

This paper describes a procedure to steer rapidly successive iterates of an initial condition on a chaotic attractor to a small target region about any prespecified point on the attractor using only small controlling perturbations. Such a procedure is called "targeting. " Previous work on targeting for chaotic attractors has been in the context of oneand two-dimensional maps. Here it is shown t...

The non-linear dynamics of a chaotic attractor offer a number of useful features to the developer of neuromorphic systems. Included in these is the ability for efficient memory storage and recall. A chaotic attractor has a potentially infinite number of Unstable Periodic Orbits (UPO) embedded within it. These orbits can be stabilised with the application of delayed feedback inhibition. This res...

When a dynamical system exhibits transient chaos and a nonchaotic attractor, as in a periodic window, noise can induce a chaotic attractor. In particular, when the noise amplitude exceeds a critical value, the largest Lyapunov exponent of the attractor of the system starts to increase from zero. While a scaling law for the variation of the Lyapunov exponent with noise was uncovered previously, ...

We model an elastic beam subject to a contact load which displaces under a chaotic external forcing, motivated by application of a ship carrying either a crane, or fluids in internal tanks. This model not only has rich dynamics and relevance in its own right, it gives rise to a Partial Differential Equation (PDE) whose solutions are chaotic, with an attractor whose points lie “near” a low-dimen...

The energy-optimal migration of a chaotic oscillator from one attractor to another coexisting attractor is investigated via an analogy between the Hamiltonian theory of fluctuations and Hamiltonian formulation of the control problem. We demonstrate both on physical grounds and rigorously that the Wentzel-Freidlin Hamiltonian arising in the analysis of fluctuations is equivalent to Pontryagin’s ...

Strange nonchaotic attractors (SNAs) were previously thought to arise exclusively in quasiperiodic dynamical systems. A recent study has revealed, however, that such attractors can be induced by noise in nonquasiperiodic discrete-time maps or in periodically driven flows. In particular, in a periodic window of such a system where a periodic attractor coexists with a chaotic saddle (nonattractin...

We show that one can use recently introduced statistics for continuity and differentiability to show the effect of filters of infinite extent in time on a chaotic time series. The statistics point to a discontinuous or nondifferentiable function between the unfiltered attractor and the filtered attractor as the origin of attractor dimension increase when the filtering is severe. The density of ...