49 research outputs found
Slower Speed and Stronger Coupling: Adaptive Mechanisms of Self-Organized Chaos Synchronization
We show that two initially weakly coupled chaotic systems can achieve
self-organized synchronization by adaptively reducing their speed and/or
enhancing the coupling strength. Explicit adaptive algorithms for
speed-reduction and coupling-enhancement are provided. We apply these
algorithms to the self-organized synchronization of two coupled Lorenz systems.
It is found that after a long-time self-organized process, the two coupled
chaotic systems can achieve synchronization with almost minimum required
coupling-speed ratio.Comment: 4 pages, 5 figure
Synchronization Based Approach for Estimating All Model Parameters of Chaotic Systems
The problem of dynamic estimation of all parameters of a model representing
chaotic and hyperchaotic systems using information from a scalar measured
output is solved. The variational calculus based method is robust in the
presence of noise, enables online estimation of the parameters and is also able
to rapidly track changes in operating parameters of the experimental system.
The method is demonstrated using the Lorenz, Rossler chaos and hyperchaos
models. Its possible application in decoding communications using chaos is
discussed.Comment: 13 pages, 4 figure
Analytical results for coupled map lattices with long-range interactions
We obtain exact analytical results for lattices of maps with couplings that
decay with distance as . We analyze the effect of the coupling
range on the system dynamics through the Lyapunov spectrum. For lattices whose
elements are piecewise linear maps, we get an algebraic expression for the
Lyapunov spectrum. When the local dynamics is given by a nonlinear map, the
Lyapunov spectrum for a completely synchronized state is analytically obtained.
The critical lines characterizing the synchronization transition are determined
from the expression for the largest transversal Lyapunov exponent. In
particular, it is shown that in the thermodynamical limit, such transition is
only possible for sufficiently long-range interactions, namely, for , where is the lattice dimension.Comment: 4 pages, 2 figures, corrections included. Phys. Rev. E 68, 045202(R)
(2003); correction in pres