Spatio-temporal pattern formation in a lateral high-frequency glow discharge system

1993 ◽  
Vol 179 (4-5) ◽  
pp. 348-354 ◽  
Author(s):  
E. Ammelt ◽  
D. Schweng ◽  
H.-G. Purwins
Keyword(s):  
Pattern Formation ◽  
Glow Discharge ◽  
High Frequency ◽  
Temporal Pattern ◽  
Discharge System ◽  
Spatio Temporal

scholarly journals Spatio-temporal Pattern Formation in Chemical Reactions

PAMM ◽  
2002 ◽  
Vol 1 (1) ◽  
pp. 16
Author(s):  
A.F. Münster ◽  
M. Seipel ◽  
S. Wolff
Keyword(s):  
Pattern Formation ◽  
Chemical Reactions ◽  
Temporal Pattern ◽  
Spatio Temporal

Spatio-temporal pattern formation, fractals, and chaos in conceptual ecological models as applied to coupled plankton-fish dynamics

2002 ◽  
Vol 172 (1) ◽  
pp. 31 ◽  
Author(s):  
Aleksandr B. Medvinskii ◽  
Sergei V. Petrovskii ◽  
Irina A. Tikhonova ◽  
D.A. Tikhonov ◽  
B.L. Li ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Temporal Pattern ◽  
Ecological Models ◽  
Spatio Temporal

BIFURCATION ANALYSIS FOR A ONE PREDATOR AND TWO PREY MODEL WITH PREY-TAXIS

2021 ◽  
Vol 29 (02) ◽  
pp. 495-524 ◽  
Author(s):  
EVAN C. HASKELL ◽  
JONATHAN BELL
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Pattern Formation ◽  
Temporal Pattern ◽  
Predator Population ◽  
Asymptotically Stable ◽  
Interaction Dynamics ◽  
Spatio Temporal ◽  
Population Interaction ◽  
Time Periodic

This paper concerns spatio-temporal pattern formation in a model for two competing prey populations with a common predator population whose movement is biased by direct prey-taxis mechanisms. By pattern formation, we mean the existence of stable, positive non-constant equilibrium states, or nontrivial stable time-periodic states. The taxis can be either repulsive or attractive and the population interaction dynamics is fairly general. Both types of pattern formation arise as one-parameter bifurcating solution branches from an unstable constant stationary state. In the absence of our taxis mechanism, the coexistence positive steady state, under suitable conditions, is locally asymptotically stable. In the presence of a sufficiently strong repulsive prey defense, pattern formation will develop. However, in the attractive taxis case, the attraction needs to be sufficiently weak for pattern formation to develop. Our method is an application of the Crandall–Rabinowitz and the Hopf bifurcation theories. We establish the existence of both types of branches and develop expressions for determining their stability.

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