The presence of chaotic transients in a nonlinear dynamo is investigated through numerical simulations the 3D magnetohydrodynamic equations. By using kinetic helicity flow as control parameter, hysteretic blowout bifurcation conjectured to be responsible for transition dynamo, leading sudden increase magnetic energy attractor. This high-energy hydromagnetic attractor suddenly destroyed boundary...

We investigate the sudden destruction of hyperchaotic attractors in symmetrically coupled onedimensional maps. An asynchronous hyperchaotic attractor may appear through a blow-out bifurcation, where the synchronous chaotic attractor on the invariant synchronization line becomes unstable with respect to perturbations transverse to the synchronization line. It is found that such a hyperchaotic at...

Recent works have demonstrated that a blowout bifurcation can lead to symmetry breaking in chaotic systems with a simple kind of symmetry. That is, as a system parameter changes, when a chaotic attractor lying in some invariant subspace becomes unstable with respect to perturbations transverse to the invariant subspace, a symmetry-broken attractor can be born. As the parameter varies further, a...

Control of chaos refers to a process wherein a tiny perturbation is applied to a chaotic system, in order to realize a desirable (chaotic, periodic, or stationary) behavior. We review the major ideas involved in the control of chaos, and present in detail two methods: the Ott}Grebogi}Yorke (OGY) method and the adaptive method. We also discuss a series of relevant issues connected with chaos con...

It is well known that dynamical systems defined by piecewise smooth functions exhibit several phenomena which cannot occur in smooth systems, such as for example, border collision bifurcations, sliding, chattering, etc. [di Bernardo et al., 2008]. One such phenomenon is the persistence of chaotic attractors under parameter perturbations, referred to as robust chaos [Banerjee et al., 1998]. In t...

An embedding of chaotic data into a suitable phase space creates a diffeomorphism of the original attractor with the reconstructed attractor. Although diffeomorphic, the original and reconstructed attractors may not be topologically equivalent. In a previous work, we showed how the original and reconstructed attractors can differ when the original is three-dimensional and of genus-one type. In ...

Recent work has considered the possibility of utilizing symbolic representations of controlled chaotic orbits for digital communication. We argue that dynamically a coding scheme usually leads to trajectories that live on a nonattracting but noise-resisting chaotic saddle embedded in the chaotic attractor. We present analyses and numerical computation which indicate that the channel capacity of...

Estimating parameters of a model system using observed chaotic scalar time series data is a topic of active interest. To estimate these parameters requires a suitable similarity indicator between the observed and model systems. Many works have considered a similarity measure in the time domain, which has limitations because of sensitive dependence on initial conditions. On the other hand, there...

The chaotic hypothesis discussed in [GC1] is tested experimentally in a simple conduction model. Besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which, as the forcing strength grows, the attractor ceases to be an Anosov system and becomes an Axiom A attractor. A first test of the new predictions is also attempted.

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists wit...