By performing a systematic study of the Hénon map, we find low-period sinks for parameter values extremely close to the classical ones. This raises the question whether or not the well-known Hénon attractor-the attractor of the Hénon map existing for the classical parameter values-is a strange attractor, or simply a stable periodic orbit. Using results from our study, we conclude that even if t...

A commercial chaotic pendulum is modified to study nonlinear dynamics, including the determination of Poincaré sections, fractal dimensions, and Lyapunov exponents. The apparatus is driven by a simple oscillating mechanism powered by a 200 pulse per revolution stepper motor running at constant angular velocity. A computer interface generates the uniform pulse train needed to run the stepper mot...

Recently, a system with uniformly hyperbolic attractor of Smale-Williams type has been suggested [Kuznetsov, Phys. Rev. Lett., 95, 144101, 2005]. This system consists of two coupled non-autonomous van der Pol oscillators and admits simple physical realization. In present paper we introduce amplitude equations for this system and prove that the attractor of the system of amplitude equations is a...

In this paper, in order to show some interesting phenomena of three dimensional autonomous ordinary differential equations, the chaotic behavior as a function of a variable control parameter, has been studied. The complex dynamical behaviors of the system are further investigated by means of eigenvalue structures and various attractors. The chaotic system examined in MATLAB 2010. The Oscillator...

It is shown how chaotic systems with more than one strange attractor can be controlled. Issues in controlling multiple (coexisting) strange attractors are stabilizing a desired motion within one attractor as well as taking the system dynamics from one attractor to another. Realization of these control objectives is demonstrated using a numerical example, the Newton–Leipnik system.  2002 Elsevi...

For different settings of a control parameter, a chaotic system can go from a region with two separate stable attractors (generalized bistability) to a crisis where a chaotic attractor expands, colliding with an unstable orbit. In the bistable regime jumps between independent attractors are mediated by external perturbations; above the crisis, the dynamics includes visits to regions formerly be...

Aerosols under chaotic advection often approach a strange attractor. They move chaotically on this fractal set but, in the presence of gravity, they have a net vertical motion downwards. In practical situations, observational data may be available only at a given level, for example, at the ground level. We uncover two fractal signatures of chaotic advection of aerosols under the action of gravi...

Attractor systems are useful in neurodynamics, mainly in the modeling of associative memory. This paper presents a complexity theory for continuous phase space dynamical systems with discrete or continuous time update, which evolve to attractors. In our framework we associate complexity classes with different types of attractors. Fixed points belong to the class BPPd, while chaotic attractors a...

The residence time around di+erent parts of a chaotic attractor is studied experimentally for nonlinear dynamical system with a double-scroll. It is shown that the dynamics of jumping from one scroll of the attractor to the other produces a distinct low-frequency peak in the otherwise featureless noise-like background produced by the chaotic dynamics. This peak can be interpreted as a distribut...

A system of non-linear difference equations is used to model the effects of density-dependent selection and migration in a population characterized by two alleles at a single gene locus. Results for the existence and stability of polymorphic equilibria are established. Properties for a genetically important class of equilibria associated with complete dominance in fitness are described. The bir...