The theoretic ground of a local-topological method for defining a minimal attractor embedding dimension on the basis of matrix decomposition is proposed. The investigation of digital electrocardio signals using local-topological analysis of chaotic attractor trajectories is carried out. The computer confirmation of the theoretical results is presented.

We study chaotic maps with multiple coexisting strange attractors and show how such systems can be controlled. To this end, a control scheme is proposed which is capable of stabilizing a desired motion within one strange attractor as well as taking the system dynamics from one strange attractor to another. To demonstrate the given control scheme, several examples are considered.

Riddling bifurcation, i.e., the bifurcation in which one of the unstable periodic orbits embedded in a chaotic attractor becomes unstable transverse to the attractor, leads to the loss of chaos synchronization in coupled identical systems. We discuss here the manifestation of the riddling bifurcation for the case of a small parameter mismatch between coupled systems. We show that for slightly n...

By tuning a control parameter, a chaotic system can either display two or more attractors (generalized multistability) or exhibit an interior crisis, whereby a chaotic attractor suddenly expands to include the region of an unstable orbit (bursting regime).Recently, control of multistability and bursting have been experimentally proved in a modulated class B laser by means of a feedback method. ...

In this paper, we present the chaotic verification for angular glint of complex radar target. Angular glint is a key factor in the generation loss probability in radar detections, and the intrinsic physical characteristic and suppression techniques of glint have been a hot topic in radar signal analysis. In this paper, the radar angular glint samples of a typical complex target are calculated b...

A crisis is a global bifurcation in which a chaotic attractor has a discontinuous change in size or suddenly disappears as a scalar parameter of the system is varied. In this Letter, we describe a global bifurcation in three dimensions which can result in a crisis. This bifurcation does not involve a tangency and cannot occur in maps of dimension smaller than 3. We present evidence of unstable ...

A symmetric chaotic flow is time-reversible if the equations governing the flow are unchanged under the transformation t → −t except for a change in sign of one or more of the state space variables. The most obvious solution is symmetric and the same in both forward and reversed time and thus cannot be dissipative. However, it is possible for the symmetry of the solution to be broken, resulting...

Chaotic transients occur in many experiments including those in fluids, in simulations of the plane Couette flow, and in coupled map lattices and they are a common phenomena in dynamical systems. Superlong chaotic transients are caused by the presence of chaotic saddles whose stable sets have fractal dimensions that are close to phase-space dimension. For many physical systems chaotic saddles h...

The results of numerical experiments on the structure of chaotic attrac-tors in the Khalatnikov-Kroyter model of two freedoms are presented. This model was developed for a qualitative description of the wave turbulence of the second sound in helium. The attractor dimension, size, and the maximal Lyapunov exponent in dependence on the single dimensionless parameter F of the model are found and d...

Recent works have considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. We show that riddling can be induced by arbitrarily small random noise even if the attractor is transversely unstable, and we obtain universal scaling laws...