131 research outputs found
The Control of Dynamical Systems - Recovering Order from Chaos -
Following a brief historical introduction of the notions of chaos in
dynamical systems, we will present recent developments that attempt to profit
from the rich structure and complexity of the chaotic dynamics. In particular,
we will demonstrate the ability to control chaos in realistic complex
environments. Several applications will serve to illustrate the theory and to
highlight its advantages and weaknesses. The presentation will end with a
survey of possible generalizations and extensions of the basic formalism as
well as a discussion of applications outside the field of the physical
sciences. Future research avenues in this rapidly growing field will also be
addressed.Comment: 18 pages, 9 figures. Invited Talk at the XXIth International
Conference on the Physics of Electronic and Atomic Collisions (ICPEAC), July
22-27, 1999 (Sendai, Japan
Constructing multiwing attractors from a robust chaotic system with non-hyperbolic equilibrium points
We investigate a three-dimensional (3D) robust chaotic system which only holds two nonhyperbolic equilibrium points, and finds the complex dynamical behaviour of position modulation beyond amplitude modulation. To extend the application of this chaotic system, we initiate
a novel methodology to construct multiwing chaotic attractors by modifying the position and amplitude parameters. Moreover, the signal amplitude, range and distance of the generated multiwings can be easily adjusted by using the control parameters, which enable us to enhance the potential application in chaotic cryptography and secure communication. The effectiveness of the theoretical analyses is confirmed by numerical simulations. Particularly, the multiwing
attractor is physically realized by using DSP (digital signal processor) chip
Predictability: a way to characterize Complexity
Different aspects of the predictability problem in dynamical systems are
reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy,
Shannon entropy and algorithmic complexity is discussed. In particular, we
emphasize how a characterization of the unpredictability of a system gives a
measure of its complexity. Adopting this point of view, we review some
developments in the characterization of the predictability of systems showing
different kind of complexity: from low-dimensional systems to high-dimensional
ones with spatio-temporal chaos and to fully developed turbulence. A special
attention is devoted to finite-time and finite-resolution effects on
predictability, which can be accounted with suitable generalization of the
standard indicators. The problems involved in systems with intrinsic randomness
is discussed, with emphasis on the important problems of distinguishing chaos
from noise and of modeling the system. The characterization of irregular
behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports.
Related information at this http://axtnt2.phys.uniroma1.i
Chaos-Based Coffee Can Radar System
Linear frequency modulated (LFM) radar systems are simple and easy to implement, making them ideal for inexpensive undergraduate research projects. Unfortunately, LFM radar schemes have multiple limitations that make them unviable in many real-world applications. Given the limitations of LFM radar systems, we propose a chaos-based frequency modulated (CBFM) system. In this paper, we present the theory, design, and experimental verification of a CBFM radar system that has both ranging and synthetic aperture radar imaging capabilities. The performance of our CBFM system is compared to that of the LFM system designed by MIT. We document many challenges and unforeseen obstacles that were encountered while developing one of the first CBFM radar systems. Although our initial results look promising, particularly for ranging, there remains a significant amount of research and development to be done on the SAR imaging signal processing software algorithms before a CBFM radar scheme is fully functional
- …