5,512 research outputs found
Hyperbolic Chaos of Turing Patterns
We consider time evolution of Turing patterns in an extended system governed
by an equation of the Swift-Hohenberg type, where due to an external periodic
parameter modulation long-wave and short-wave patterns with length scales
related as 1:3 emerge in succession. We show theoretically and demonstrate
numerically that the spatial phases of the patterns, being observed
stroboscopically, are governed by an expanding circle map, so that the
corresponding chaos of Turing patterns is hyperbolic, associated with a strange
attractor of the Smale-Williams solenoid type. This chaos is shown to be robust
with respect to variations of parameters and boundary conditions.Comment: 4 pages, 4 figure
Numerical test for hyperbolicity of chaotic dynamics in time-delay systems
We develop a numerical test of hyperbolicity of chaotic dynamics in
time-delay systems. The test is based on the angle criterion and includes
computation of angle distributions between expanding, contracting and neutral
manifolds of trajectories on the attractor. Three examples are tested. For two
of them previously predicted hyperbolicity is confirmed. The third one provides
an example of a time-delay system with nonhyperbolic chaos.Comment: 7 pages, 5 figure
Features of pulsed synchronization of a systems with a tree-dimensional phase space
Features of synchronization picture in the system with the limit cycle
embedded in a three-dimensional phase space are considered. By the example of
Ressler system and Dmitriev - Kislov generator under the action of a periodic
sequence of delta - function it is shown, that synchronization picture
significantly depends on the direction of pulse action. Features of
synchronization tons appeared in these models are observed.Comment: 16 pages, 11 figure
- …