2,698 research outputs found
Extension of Lorenz Unpredictability
It is found that Lorenz systems can be unidirectionally coupled such that the
chaos expands from the drive system. This is true if the response system is not
chaotic, but admits a global attractor, an equilibrium or a cycle. The
extension of sensitivity and period-doubling cascade are theoretically proved,
and the appearance of cyclic chaos as well as intermittency in interconnected
Lorenz systems are demonstrated. A possible connection of our results with the
global weather unpredictability is provided.Comment: 32 pages, 13 figure
Generalized synchronization onset
The behavior of two unidirectionally coupled chaotic oscillators near the
generalized synchronization onset has been considered. The character of the
boundaries of the generalized synchronization regime has been explained by
means of the modified systemComment: 7 pages, 3 figure
Bifurcation and Chaos in Coupled Ratchets exhibiting Synchronized Dynamics
The bifurcation and chaotic behaviour of unidirectionally coupled
deterministic ratchets is studied as a function of the driving force amplitude
() and frequency (). A classification of the various types of
bifurcations likely to be encountered in this system was done by examining the
stability of the steady state in linear response as well as constructing a
two-parameter phase diagram in the () plane. Numerical explorations
revealed varieties of bifurcation sequences including quasiperiodic route to
chaos. Besides, the familiar period-doubling and crises route to chaos
exhibited by the one-dimensional ratchet were also found. In addition, the
coupled ratchets display symmetry-breaking, saddle-nodes and bubbles of
bifurcations. Chaotic behaviour is characterized by using the sensitivity to
initial condition as well as the Lyapunov exponent spectrum; while a perusal of
the phase space projected in the Poincar cross-section confirms some
of the striking features.Comment: 7 pages; 8 figure
Rapid convergence of time-averaged frequency in phase synchronized systems
Numerical and experimental evidence is presented to show that many phase
synchronized systems of non-identical chaotic oscillators, where the chaotic
state is reached through a period-doubling cascade, show rapid convergence of
the time-averaged frequency. The speed of convergence toward the natural
frequency scales as the inverse of the measurement period. The results also
suggest an explanation for why such chaotic oscillators can be phase
synchronized.Comment: 6 pages, 9 figure
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