scholarly journals A model of self-organized motion pattern formation

2010 ◽  
Vol 1 (3) ◽  
pp. 371-371
Author(s):  
H. S. Hock ◽  
C. L. Park ◽  
G. Schoner
Keyword(s):  
Pattern Formation ◽  
Motion Pattern ◽  
Self Organized

Active-Site Motion and Pattern Formation in Self-Organized Interface Depinning

1996 ◽  
Vol 76 (3) ◽  
pp. 423-426 ◽  
Author(s):  
Supriya Krishnamurthy ◽  
Mustansir Barma
Keyword(s):  
Pattern Formation ◽  
Active Site ◽  
Self Organized

Instabilities and pattern formation during the self-organized growth of nanoparticles on graphite

2002 ◽  
Vol 496 (1-2) ◽  
pp. L18-L22 ◽  
Author(s):  
Bernhard Kaiser ◽  
Bert Stegemann ◽  
Hanna Kaukel ◽  
Klaus Rademann
Keyword(s):  
Pattern Formation ◽  
The Self ◽  
Self Organized

scholarly journals Self-organized pattern formation in motor-microtubule mixtures

2004 ◽  
Vol 70 (3) ◽  
Author(s):  
Sumithra Sankararaman ◽  
Gautam I. Menon ◽  
P. B. Sunil Kumar
Keyword(s):  
Pattern Formation ◽  
Self Organized

Bifurcation Dynamics and Pattern Formation of a Three-Species Food Chain System with Discrete Spatiotemporal Variables

2019 ◽  
Vol 74 (11) ◽  
pp. 945-959
Author(s):  
Huayong Zhang ◽  
Ge Pan ◽  
Tousheng Huang ◽  
Tianxiang Meng ◽  
Jieru Wang ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Food Chain ◽  
Complex Dynamics ◽  
Period Doubling ◽  
Turing Instability ◽  
Flip Bifurcation ◽  
Chain System ◽  
Self Organized ◽  
New Perspective ◽  
Centre Manifold Theorem

AbstractThe bifurcation dynamics and pattern formation of a discrete-time three-species food chain system with Beddington–DeAngelis functional response are investigated. Via applying the centre manifold theorem and bifurcation theorems, the occurrence conditions for flip bifurcation and Neimark–Sacker bifurcation as well as Turing instability are determined. Numerical simulations verify the theoretical results and reveal many interesting dynamic behaviours. The flip bifurcation and the Neimark–Sacker bifurcation both induce routes to chaos, on which we find period-doubling cascades, invariant curves, chaotic attractors, sub–Neimark–Sacker bifurcation, sub–flip bifurcation, chaotic interior crisis, sub–period-doubling cascade, periodic windows, sub–periodic windows, and various periodic behaviours. Moreover, the food chain system exhibits various self-organized patterns, including regular and irregular patterns of stripes, labyrinth, and spiral waves, suggesting the populations can coexist in space as many spatiotemporal structures. These analysis and results provide a new perspective into the complex dynamics of discrete food chain systems.

A mathematical model of self-organized pattern formation on the combs of honeybee colonies

1990 ◽  
Vol 147 (4) ◽  
pp. 553-571 ◽  
Author(s):  
Scott Camazine ◽  
James Sneyd ◽  
Michael J. Jenkins ◽  
J.D. Murray
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Self Organized
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