Fractal formations in the Lattice Limit Cycle model |
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Authors: | G A Tsekouras A Provata |
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Institution: | (1) Institute of Physical Chemistry, National Center for Scientific Research “Demokritos”, 15310 Athens, Greece;(2) Department of Physics, University of Athens, 10679 Athens, Greece |
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Abstract: | We examine the fractal patterns arising in the Lattice Limit Cycle model, when it
is restricted on square and fractal lattices.
We show that, for processes taking place on regular 2d substrates, the
fractal dimensions depend on the kinetic constants and we have observed
a sharp phase-transition from uniform 2d spatial distributions (df=2)
when the kinetic parameters are near the Hopf bifurcation point, to a
inside the limit cycle region.
For processes taking place on substrates which contain inactive sites,
we observe nucleation
of homologous species around inactive regions leading to poisoning,
when the active sites are distributed in a fractal manner on the substrate.
This is less frequent in cases where the active sites are distributed
uniformly and randomly on the lattice leading, normally,
to non-trivial steady states. |
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Keywords: | 05 45 -a Nonlinear dynamics and chaos 05 45 Df Fractals 05 65 +b Self-organized systems |
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