Spatial chaos of traveling waves has a given velocity

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 80, Issue 2, 2009, Pages

  Fernandez, Bastien ^a   Luna, Beatriz ^b   Ugalde, Edgardo ^b  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

^b UNIVERSIDAD AUTÓNOMA DE SAN LUIS POTOSÍ   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

ENTROPY; TOPOLOGY;

ARBITRARY VELOCITIES; COUPLED MAP LATTICES; EXTENDED SYSTEMS; NUMERICAL CALCULATION; SYMBOLIC DYNAMICS; TOPOLOGICAL ENTROPY; TRAVELING WAVE; VELOCITY-DEPENDENT;

VELOCITY;

EID: 70349247821     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.025203     Document Type: Article

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18. By Eq. 2, the corresponding orbit coordinates write xst =φ (s-vt) where the profile is defined by φ (z) = σ k=1 σ n=0 k l n,k θ θ z-n+vk ⌋.
19. For numerical purposes, the TW entropy is defined here as the exponential growth rate of the number PL,v of L -periodic patterns with a given velocity v, i.e., lim supL→ 1 ln PL,v L. This quantity is related to the standard topological entropy based on the number of admissible words, see, e.g., R. Badii and A. Politi, Complexity: Hierarchical Structures and Scaling in Physics (Cambridge University Press, New York, 1997).
20. Because of contraction, any orbit remaining at bounded distance of discontinuities (as for all orbits considered here) is Lyapunov stable and thus structurally stable.
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23. For any T<1- l0 = σ n=1 1 ln, we have T≤ σ n=1 L ln for L large enough. Thus, every fixed-point pattern containing a (finite) 1-block of length L or larger cannot be admissible and the fixed-point entropy must be smaller than ln(2).
24. For instance fronts with velocity v≠1/2 coexist together with a chaotic set of waves with velocity 1/2 in the central bottom domain D1/2 of Fig. 1.