105 research outputs found
Route to hyperchaos in Rayleigh-Benard convection
Transition to hyperchaotic regimes in Rayleigh-Benard convection in a square
periodicity cell is studied by three-dimensional numerical simulations. By
fixing the Prandtl number at P=0.3 and varying the Rayleigh number as a control
parameter, a bifurcation diagram is constructed where a route to hyperchaos
involving quasiperiodic regimes with two and three incommensurate frequencies,
multistability, chaotic intermittent attractors and a sequence of boundary and
interior crises is shown. The three largest Lyapunov exponents exhibit a linear
scaling with the Rayleigh number and are positive in the final hyperchaotic
attractor. Thus, a route to weak turbulence is found
Bifurcation structures and transient chaos in a four-dimensional Chua model
A four-dimensional four-parameter Chua model with cubic nonlinearity is
studied applying numerical continuation and numerical solutions methods.
Regarding numerical solution methods, its dynamics is characterized on Lyapunov
and isoperiodic diagrams and regarding numerical continuation method, the
bifurcation curves are obtained. Combining both methods the bifurcation
structures of the model were obtained with the possibility to describe the {\it
shrimp}-shaped domains and their endoskeletons. We study the effect of a
parameter that controls the dimension of the system leading the model to
present transient chaos with its corresponding basin of attraction being
riddled.Comment: 9 figures, to appear in PL
Hyperchaotic attractors of three-dimensional maps and scenarios of their appearance
We study bifurcation mechanisms of the appearance of hyperchaotic attractors
in three-dimensional maps. We consider, in some sense, the simplest cases when
such attractors are homoclinic, i.e. they contain only one saddle fixed point
and entirely its unstable manifold. We assume that this manifold is
two-dimensional, which gives, formally, a possibility to obtain two positive
Lyapunov exponents for typical orbits on the attractor (hyperchaos). For
realization of this possibility, we propose several bifurcation scenarios of
the onset of homoclinic hyperchaos that include cascades of both supercritical
period-doubling bifurcations with saddle periodic orbits and supercritical
Neimark-Sacker bifurcations with stable periodic orbits, as well as various
combinations of these cascades. In the paper, these scenarios are illustrated
by an example of three-dimensional Mir\'a map.Comment: 40 pages, 24 figure
Simple 4d – Hyperchaotic Canonical Van der pol Duffing Oscillator using Current Feedback Op-Amp
In this paper, in order to show some interesting phenomena of fourth-order hyperchaotic Canonical Van der Pol Duffing oscillator circuit with a smooth cubic nonlinearity, different kinds of attractors, time waveforms and corresponding Lyapunov exponent spectra of systems are presented, respectively. The perturbation transforms an unpredictable hyperchaotic behavior into a predictable hyperchaotic or periodic motion via stabilization of unstable, aperiodic, or periodic orbits of the strange hyperchaotic attractor. One advantage of the method is its robustness against noise. A theoretical analysis of the circuit equations is presented, along with experimental simulation and numerical results
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