We study some properties of pattern formation arising in large arrays of locally coupled first-order nonlinear dynamical systems, namely Cellular Neural Networks (CNNs). We will present exact results to analyze spatial patterns for symmetric coupling and to analyze spatio-temporal patterns for anti-symmetric coupling in one-dimensional lattices, which will then be completed by approximative results based on a spatial and/or temporal frequency approach. We will discuss the validity of these approximations, which bring a lot of insight. This spectral approach becomes very convenient for the two-dimensional lattice, as exact results get more complicated to establish. In this second part, we will only consider a symmetric coupling between cells. We will show what kinds of motifs can be found in the patterns generated by 3 x 3 templates. Then, we will discuss the dynamics of pattern formation starting from initial conditions which are a small random noise added to the unstable equilibrium: this can generally be well predicted by the spatial frequency approach. We will also study whether a defect in a pure pattern can propagate or not through the whole lattice, starting from initial conditions being a localized perturbation of a stable pattern: this phenomenon is no longer correctly predicted by the spatial frequency approach. We also show that patterns such as spirals and targets can be formed by ''seed'' initial conditions - localized, non-random perturbations of an unstable equilibrium. Finally, the effects on the patterns formed of a bias term in the dynamics are demonstrated.
Characterization and Dynamics of Pattern Formation in Cellular Neural Networks / Crounse, K. R.; Chua, L. O.; Thiran, P.; Setti, G.. - In: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING. - ISSN 0218-1274. - 6:(1996), pp. 1703-1724. [10.1142/S0218127496001053]
|Titolo:||Characterization and Dynamics of Pattern Formation in Cellular Neural Networks|
|Data di pubblicazione:||1996|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1142/S0218127496001053|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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