Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators

We present three examples how complex spatio-temporal patterns can be linked to hyperchaotic attractors in dynamical systems consisting of nonlinear biochemical oscillators coupled linearly with diffusion terms. The systems involved are: (a) a two-variable oscillator with two consecutive autocatalytic reactions derived from the Lotka–Volterra scheme; (b) a minimal two-variable oscillator with one first-order autocatalytic reaction; (c) a three-variable oscillator with first-order feedback lacking autocatalysis. The dynamics of a finite number of coupled biochemical oscillators may account for complex patterns in compartmentalized living systems like cells or tissue, and may be tested experimentally in coupled microreactors.

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On the regularity of many-particle dynamical systems perturbed by white noise

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953396000378 ◽

1996 ◽

Vol 9 (4) ◽

pp. 427-437 ◽

Cited By ~ 3

Author(s):

Anatoli V. Skorokhod

Keyword(s):

Dynamical Systems ◽

Finite Number ◽

White Noise ◽

Interaction Force ◽

The Other ◽

Inertial Particles ◽

First Order ◽

Random Forces ◽

Diffusion Motion ◽

Number Of Particles

We consider a system of finite number of particles that are moving in Rd under mutual interaction. It is assumed that the particles are subjected to some additional random forces which cause diffusion motion of the particles. The latter is described by a system of stochastic differential equations of the first order for noninertia particles and the second order for inertial particles. The coefficient of the system are unbounded because the interaction force tends to infinity if the distance between two particles tends to zero. The system is called regular if no particle can hit the other. We investigate conditions of regularity.This article is dedicated to the memory of Roland L. Dobrushin.

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CLUSTERING-BASED APPROACHES TO THE EXPLORATION OF SPATIO-TEMPORAL DATA

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xlii-2-w7-1387-2017 ◽

2017 ◽

Vol XLII-2/W7 ◽

pp. 1387-1391 ◽

Cited By ~ 1

Author(s):

X. Wu ◽

R. Zurita-Milla ◽

M.-J. Kraak ◽

E. Izquierdo-Verdiguier

Keyword(s):

Clustering Algorithm ◽

Clustering Algorithms ◽

Temporal Patterns ◽

Data Cube ◽

Data Matrix ◽

Temporal Data Mining ◽

Temporal Data ◽

Complex Patterns ◽

Spatio Temporal ◽

Temporal Dimensions

As one spatio-temporal data mining task, clustering helps the exploration of patterns in the data by grouping similar elements together. However, previous studies on spatial or temporal clustering are incapable of analysing complex patterns in spatio-temporal data. For instance, concurrent spatio-temporal patterns in 2D or 3D datasets. In this study we present two clustering algorithms for complex pattern analysis: (1) the Bregman block average co-clustering algorithm with I-divergence (BBAC_I) which enables the concurrent analysis of spatio-temporal patterns in 2D data matrix, and (2) the Bregman cube average tri-clustering algorithm with I-divergence (BCAT_I) which enables the complete partitional analysis in 3D data cube. Here the use of the two clustering algorithms is illustrated by Dutch daily average temperature dataset from 28 weather stations from 1992 to 2011. For BBAC_I, it is applied to the averaged yearly dataset to identify station-year co-clusters which contain similar temperatures along stations and years, thus revealing patterns along both spatial and temporal dimensions. For BCAT_I, it is applied to the temperature dataset organized in a data cube with one spatial (stations) and two nested temporal dimensions (years and days). By partitioning the whole dataset into clusters of stations and years with similar within-year temperature similarity, BCAT_I explores the spatio-temporal patterns of intra-annual variability in the daily temperature dataset. As such, both BBAC_I and BCAT_I algorithms, combined with suitable geovisualization techniques, allow the exploration of complex spatial and temporal patterns, which contributes to a better understanding of complex patterns in spatio-temporal data.

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