6533b857fe1ef96bd12b4306
RESEARCH PRODUCT
FLUCTUATION-INDUCED LOCAL OSCILLATIONS AND FRACTAL PATTERNS IN THE LATTICE LIMIT CYCLE MODEL
A. ShabuninFotios K. DiakonosFlorence BarasFlorence BarasVladimir AstakhovG. A. TsekourasAstero ProvataDimitri J. Frantzeskakissubject
Hopf bifurcationGeneral MathematicsMathematical analysisGeneral Physics and AstronomyFractal landscapeParameter spaceSquare latticeFractal dimensionsymbols.namesakeFractalFractal derivativeLimit cyclesymbolsMathematicsdescription
The fractal properties of the Lattice Limit Cycle model are explored when the process is realized on a 2-dimensional square lattice support via Monte Carlo Simulations. It is shown that the structure of the steady state presents inhomogeneous fluctuations in the form of domains of identical particles. The various domains compete with one another via their borders which have self-similar, fractal structure. The fractality is more prominent, (fractal dimensions df < 2), when the parameter values are near the critical point where the Hopf bifurcation occurs. As the distance from the Hopf bifurcation increases in the parameter space the system becomes more homogeneous and the fractal dimension tends to the value df = 2.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-06-01 | Fluctuation and Noise Letters |