1,944 research outputs found
Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories
Dynamical equations are formulated and a numerical study is provided for
self-oscillatory model systems based on the triple linkage hinge mechanism of
Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic
mechanical constraint of three rotators as well as systems, where three
rotators interact by potential forces. We present and discuss some quantitative
characteristics of the chaotic regimes (Lyapunov exponents, power spectrum).
Chaotic dynamics of the models we consider are associated with hyperbolic
attractors, at least, at relatively small supercriticality of the
self-oscillating modes; that follows from numerical analysis of the
distribution for angles of intersection of stable and unstable manifolds of
phase trajectories on the attractors. In systems based on rotators with
interacting potential the hyperbolicity is violated starting from a certain
level of excitation.Comment: 30 pages, 18 figure
Thresholds of Spatially Coupled Systems via Lyapunov's Method
The threshold, or saturation phenomenon of spatially coupled systems is
revisited in the light of Lyapunov's theory of dynamical systems. It is shown
that an application of Lyapunov's direct method can be used to quantitatively
describe the threshold phenomenon, prove convergence, and compute threshold
values. This provides a general proof methodology for the various systems
recently studied. Examples of spatially coupled systems are given and their
thresholds are computed.Comment: 6 page
Controlling chaos in spatially extended beam-plasma system by the continuous delayed feedback
In present paper we discuss the control of complex spatio-temporal dynamics
in a {spatially extended} non-linear system (fluid model of Pierce diode) based
on the concepts of controlling chaos in the systems with few degrees of
freedom. A presented method is connected with stabilization of unstable
homogeneous equilibrium state and the unstable spatio-temporal periodical
states analogous to unstable periodic orbits of chaotic dynamics of the systems
with few degrees of freedom. We show that this method is effective and allows
to achieve desired regular dynamics chosen from a number of possible in the
considered system.Comment: 12 pages, 12 figure
PVT-Robust CMOS Programmable Chaotic Oscillator: Synchronization of Two 7-Scroll Attractors
Designing chaotic oscillators using complementary metal-oxide-semiconductor (CMOS) integrated circuit technology for generating multi-scroll attractors has been a challenge. That way, we introduce a current-mode piecewise-linear (PWL) function based on CMOS cells that allow programmable generation of 2–7-scroll chaotic attractors. The mathematical model of the chaotic oscillator designed herein has four coefficients and a PWL function, which can be varied to provide a high value of the maximum Lyapunov exponent. The coefficients are implemented electronically by designing operational transconductance amplifiers that allow programmability of their transconductances. Design simulations of the chaotic oscillator are provided for the 0.35μ m CMOS technology. Post-layout and process–voltage–temperature (PVT) variation simulations demonstrate robustness of the multi-scroll chaotic attractors. Finally, we highlight the synchronization of two seven-scroll attractors in a master–slave topology by generalized Hamiltonian forms and observer approach. Simulation results show that the synchronized CMOS chaotic oscillators are robust to PVT variations and are suitable for chaotic secure communication applications.Universidad Autónoma de Tlaxcala CACyPI-UATx-2017Program to Strengthen Quality in Educational Institutions C/PFCE-2016-29MSU0013Y-07-23National Council for Science and Technology 237991 22284
Multifractal burst in the spatio-temporal dynamics of jerky flow
The collective behavior of dislocations in jerky flow is studied in Al-Mg
polycrystalline samples subjected to constant strain rate tests. Complementary
dynamical, statistical and multifractal analyses are carried out on the
stress-time series recorded during jerky flow to characterize the distinct
spatio-temporal dynamical regimes. It is shown that the hopping type B and the
propagating type A bands correspond to chaotic and self-organized critical
states respectively. The crossover between these types of bands is identified
by a large spread in the multifractal spectrum. These results are interpreted
on the basis of competing scales and mechanisms.Comment: 4 pages, 6 figures To be published in Phys. Rev. Lett. (2001
Permanent Magnet Synchronous Motors are Globally Asymptotically Stabilizable with PI Current Control
This note shows that the industry standard desired equilibrium for permanent
magnet synchronous motors (i.e., maximum torque per Ampere) can be globally
asymptotically stabilized with a PI control around the current errors, provided
some viscous friction (possibly small) is present in the rotor dynamics and the
proportional gain of the PI is suitably chosen. Instrumental to establish this
surprising result is the proof that the map from voltages to currents of the
incremental model of the motor satisfies some passivity properties. The
analysis relies on basic Lyapunov theory making the result available to a wide
audience
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