Inferring local dynamics and connectivity of spatially extended systems with long-range links based on steady-state stabilization

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

Volumn 82, Issue 2, 2010, Pages

  Yu, Dongchuan ^a   Parlitz, Ulrich ^b  

^a UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FITZHUGH-NAGUMO MODEL; IDENTIFICATION PROCEDURE; LOCAL DYNAMICS; LONG-RANGE LINKS; SPATIALLY EXTENDED SYSTEMS; STRUCTURAL INHOMOGENEITIES; SYSTEM IDENTIFICATIONS;

STABILIZATION;

EID: 77956097637     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.026108     Document Type: Article

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33. Here and hereafter the distance between two point sets is equal to the minimal distance between any two points which are taken from different sets.
34. We suggest here only a five-point Laplacian approximation. One could also use a higher order one (e.g., nine-point Laplacian operator).
35. If only Γ is unknown, then one may follow the methods introduced in Sec. for estimating the value of Γ.
36. In practice, one can first choose a small gain θ and then increase θ gradually until the distance between the sets I 0 and I 1 is larger than the maximal value of set I 0 and thus the sets I 0 and I 1 are distinguishable. In this way, one may determine the critical value θ c.