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Volumn 78, Issue 4, 2008, Pages

Nonlocal Ginzburg-Landau equation for cortical pattern formation

Author keywords

[No Author keywords available]

Indexed keywords

AMPLITUDE EQUATIONS; BIFURCATION PARAMETERS; CONDUCTION VELOCITIES; COUPLING STRENGTHS; DYNAMICAL INSTABILITIES; GL EQUATIONS; LANDAU EQUATIONS; LOCAL NETWORKS; LOCAL PARTS; NONLOCAL COUPLINGS; PATTERN FORMATIONS; PERTURBATION EXPANSIONS; PRIMARY VISUAL CORTICES; PROPAGATION DELAYS; RECURRENT NETWORKS; SPATIAL CORRELATIONS; SPONTANEOUS PATTERN FORMATIONS; TUNING PROPERTIES; VISUAL STIMULUS;

EID: 55849132525     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.78.041916     Document Type: Article
Times cited : (21)

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    • The dispersion relation 4.20 with λ± = ρ± +i ω± is in fact symmetric with respect to the transformation ω± →± ω± so that standing waves could also occur.
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    • note
    • One way to handle this infinite degeneracy is to restrict the space of solutions to that of doubly periodic functions corresponding to regular tilings of the plane. The original Euclidean symmetry group is then restricted to the symmetry group of the underlying lattice. In particular, there are only a finite number of rotations and reflections to consider for each lattice (modulo an arbitrary rotation of the whole plane), which correspond to the so-called holohedries of the plane. Consequently the corresponding space of marginally stable modes is now finite-dimensional-we can only rotate eigenfunctions through a finite set of angles (for example, multiples of n/2 for a square lattice and multiples of n/3 for an hexagonal lattice). The linear eigenmodes now consist of a finite linear combination of either even (+) or odd (-) stationary plane waves z (r) = n=1 N e-2i φn [cn ei kn r ± c̄ n e-i kn r]. Here N=2 for a square or rhombic lattice and N=3 for an hexagonal lattice. Also k1 k2 = kc2 cos φ with φ=π/2 for N=2, and φ=2π/3 for N=3 with k3 =- k1 - k2. Note that perturbation methods can be used to derive amplitude equations for the coefficients cn, although the basic structure of these equations can be deduced using symmetry arguments.
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.