Two-dimensional spatio-temporal dynamics of analog image processing neural networks

1995 ◽  
Vol 6 (5) ◽  
pp. 1148-1164 ◽  
Author(s):  
H. Kobayashi ◽  
T. Matsumoto ◽  
J. Sanekata
Keyword(s):  
Neural Networks ◽  
Image Processing ◽  
Temporal Dynamics ◽  
Two Dimensional ◽  
Spatio Temporal ◽  
Analog Image Processing

scholarly journals Modeling the Spatio-Temporal Dynamics of a Population with Age Structure and Long-Range Interactions: Synchronization and Clustering

2019 ◽  
Vol 14 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Matvey Kulakov ◽  
E.Ya. Frisman
Keyword(s):  
Mathematical Model ◽  
Model Equation ◽  
Temporal Dynamics ◽  
Local Population ◽  
Two Dimensional ◽  
Attraction Basin ◽  
Local Populations ◽  
Long Range Interactions ◽  
Spatio Temporal ◽  
Formation Of Groups

The paper proposed a mathematical model for spatio-temporal dynamics of two-age populations coupled by migration living on a two-dimensional areal. The model equation is a system of nonlocal coupled two-dimensional maps. We considered cases when populations are coupled in a certain neighborhood of different form: circle, square or rhombus. Special attention is paid to the situation when the intensity of the migrants flow between the territories decreases with increasing distance between them. For this model we study the conditions for the formation of groups of synchronous populations or clusters that form, in space, typical structures like spots or stripes mixed with solitary states. It is shown that the dynamics, in time, of different clusters may differ significantly and may not be coherent and correspond to several simultaneous multistable regimes or potential states of the local population. Such spatio-temporal regimes are forced and are caused by impacts or perturbations on a single or several populations when their number falls into the attraction basin of another regime. With strong coupling, such clusters are rare and are represented by single outbursts or solitary states. However, the decrease in the coupling strength leads to the fact that these outbursts cause oscillations of their neighbors, and in their neighborhood a cluster of solitary states is formed which is surrounded by subpopulations with a different type of dynamics. It was found that the interaction of different type of clusters leads to the formation of a large number of groups with transitional dynamics that were not described for local populations.

Local Complexity and Global Nonlinear Modes in Large Arrays of Fluid-Elastic Oscillators

2002 ◽  
Author(s):  
Masaharu Kuroda ◽  
Francis C. Moon
Keyword(s):  
Temporal Dynamics ◽  
Soliton Solutions ◽  
Quantitative Measure ◽  
Entropy Measure ◽  
Accelerometer Data ◽  
Two Dimensional ◽  
Elastic Rod ◽  
Local Complexity ◽  
Spatio Temporal ◽  
Elliptical Motion

Transition from local complexity to global spatio-temporal dynamics in a two dimensional array of fluid-elastic oscillators is examined experimentally with an apparatus comprising 90–1000 cantilevered rods in a wind tunnel. Wave-like behavior is observed which may be related to soliton solutions in nonlinear arrays of nonlinear oscillators. The 90 to 1000 steel and polycarbonate rods have gap ratios ranging from 1.0 to 2.5. As the Reynolds number (based on rod diameter) increases from 200 to 900, a pattern with characteristics of spatio-temporal chaos emerges in global behavior of the elastic-rod array. There are local and global patterns. Local patterns comprise transient rest, linear motion, and elliptical motion. In 90-rod experiments, a cluster-pattern entropy measure based on these three patterns is introduced as a quantitative measure of local complexity. No significant dynamics appear below a threshold wind velocity. Video images reveal that, at first, each rod moves individually; then clusters consisting of several rods emerge. Finally, global wave-like motion occurs at higher flow velocities. Spatial patterns in rod-density distribution appear as more rods impact with their nearest neighbors. Furthermore, these collective nonlinear motions of rods are observed and categorized into several global modes. Using accelerometer data, the rod impact rate versus flow velocity shows a power-law scaling relation. This phenomenon may have application to plant-wind dynamics and damage as well as heat exchangers in energy systems. This experiment may also be a two dimensional analog of impact dynamics of granular materials in a flow.

ON THE SPATIO-TEMPORAL DYNAMICS OF A CLASS OF CELLULAR NEURAL NETWORKS

2003 ◽  
Vol 12 (04) ◽  
pp. 399-416 ◽  
Author(s):  
LIVIU GORAŞ ◽  
TIBERIU DINU TEODORESCU ◽  
ROMEO GHINEA
Keyword(s):  
Neural Networks ◽  
Linear Theory ◽  
Computer Simulations ◽  
Temporal Dynamics ◽  
Linear Part ◽  
Cellular Neural Networks ◽  
Turing Patterns ◽  
Root Locus ◽  
Spatio Temporal ◽  
The Stability

The stability and dynamics of a class of Cellular Neural Networks (CNNs) in the central linear part is investigated using the decoupling technique based on discrete spatial transforms, Nyquist and root locus techniques. The influence of the cell order and template neighborhood is discussed and computer simulations are presented. It is shown that, as in the case of Turing patterns, for 1D CNNs, the patterns predicted by the linear theory of the decoupling technique are often valid even when the nonlinearity has been reached.

scholarly journals Modulated waves in a periodically driven annular cavity

2010 ◽  
Vol 667 ◽  
pp. 336-357 ◽  
Author(s):  
H. M. BLACKBURN ◽  
J. M. LOPEZ
Keyword(s):  
Symmetry Group ◽  
Temporal Dynamics ◽  
Travelling Waves ◽  
Temporal Structure ◽  
Three Dimensional ◽  
Spanwise Direction ◽  
Two Dimensional ◽  
Periodically Driven ◽  
Spatio Temporal ◽  
Temporal Symmetry

Time-periodic flows with spatio-temporal symmetry Z2 × O(2) – invariance in the spanwise direction generating the O(2) symmetry group and a half-period-reflection symmetry in the streamwise direction generating a spatio-temporal Z2 symmetry group – are of interest largely because this is the symmetry group of periodic laminar two-dimensional wakes of symmetric bodies. Such flows are the base states for various three-dimensional instabilities; the periodically shedding two-dimensional circular cylinder wake with three-dimensional modes A and B being the generic example. However, it is not easy to physically realize the ideal flows owing to the presence of end effects and finite spanwise geometries. Flows past rings are sometimes advanced as providing a relevant idealization, but in fact these have symmetry group O(2) and only approach Z2 × O(2) symmetry in the infinite aspect ratio limit. The present work examines physically realizable periodically driven annular cavity flows that possess Z2 × O(2) spatio-temporal symmetry. The flows have three distinct codimension-1 instabilities: two synchronous modes (A and B), and two manifestations of a quasi-periodic (QP) mode, either as modulated standing waves or modulated travelling waves. It is found that the curvature of the system can determine which of these modes is the first to become unstable with increasing Reynolds number, and that even in the nonlinear regime near onset of three-dimensional instabilities the dynamics are dominated by mixed modes with complicated spatio-temporal structure. Supplementary movies illustrating the spatio-temporal dynamics are available at journals.cambridge.org/flm.

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