A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.

We calculate all piecewise-constant periodic orbits (with values ±1) of the renormalisation recursion arising in the analysis of correlations of the orbit of a point on a strange nonchaotic attractor. Our results make rigorous and generalise previous numerical results.

Interior crises are understood as discontinuous changes of the size of a chaotic attractor that occur when an unstable periodic orbit collides with the chaotic attractor. We present here numerical evidence and theoretical reasoning which prove the existence of a chaos-chaos transition in which the change of the attractor size is sudden but continuous. This occurs in the Hindmarsh-Rose model of ...

This paper investigates a Hopfield neural network under the simulation of external electromagnetic radiation and dual bias currents, in which fluctuation magnetic flux across neuron membrane is used to emulate influence radiation. Utilizing conventional analytical methods, basic properties proposed are discussed. Due addition shows high sensitivity system parameters initial conditions. The poss...

We present an elementary derivation of chaos control with simple limiters using the logistic map and the Henon map as examples. This derivation provides conditions for optimal stabilization of unstable periodic orbits of a chaotic attractor.

We consider a deconvolution model for 3D periodic flows. We show the existence of a global attractor for the model. MCS Classification : 76D05, 35Q30, 76F65, 76D03 Key-words : Navier-Stokes equations, Large eddy simulation, Deconvolution models.

A method for controlling unstable periodic orbits (UPOs) that have not been controllable before is presented. The method is based on detecting UPOs that are situated outside the skeleton of a chaotic attractor. The main idea is to exploit flexible parts of the attractor, which under weak external perturbations allow variable excursions of the trajectory away from its originally determined path....

We perform a numerical study of the breakdown of hyperbolicity of quasi-periodic attractors in the dissipative standard map. In this study, we compute the quasi-periodic attractors together with their stable and tangent bundles. We observe that the loss of normal hyperbolicity comes from the collision of the stable and tangent bundles of the quasi-periodic attractor. We provide numerical eviden...