Differential flow instability in dynamical systems without an unstable (activator) subsystem

1994 ◽  
Vol 72 (13) ◽  
pp. 2017-2020 ◽  
Author(s):  
Arkady B. Rovinsky ◽  
Michael Menzinger
Keyword(s):  
Dynamical Systems ◽  
Flow Instability ◽  
Differential Flow

scholarly journals Nonlinear Analysis in a Nutrient-Algae-Zooplankton System with Sinking of Algae

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Chuanjun Dai ◽  
Min Zhao
Keyword(s):  
Numerical Simulation ◽  
Nonlinear Analysis ◽  
Spatial Patterns ◽  
Flow Instability ◽  
Reaction Diffusion ◽  
Spatial Domain ◽  
Nutrient Concentrations ◽  
Turing Bifurcation ◽  
Differential Flow ◽  
The Impact

A reaction-diffusion-advection model is proposed for the Zeya Reservoir to study interactions between algae and zooplankton, including the diffusive spread of algae and zooplankton and the sinking of algae. The model is investigated both with and without sinking. Conditions of Hopf and Turing bifurcation in the spatial domain are obtained, and conditions for differential-flow instability that gives rise to the formation of spatial patterns are derived. Using numerical simulation, the authors examine the impacts on algae of different nutrient concentrations, different sinking rates, and various diffusive spreading patterns. Finally, the models with and without sinking are compared, revealing that the sinking of algae plays an important role in the oscillations of algae and zooplankton. All these results may help to achieve a better understanding of the impact of algae in the Zeya Reservoir.

Differential flow instability in the Ginzburg-Landau and Swift-Hohenberg approximations

1996 ◽  
Vol 95 (3-4) ◽  
pp. 306-318 ◽  
Author(s):  
Arkady Rovinsky ◽  
Anatoly Malevanets ◽  
Michael Menzinger
Keyword(s):  
Flow Instability ◽  
Ginzburg Landau ◽  
Differential Flow

scholarly journals Nonlinear dynamic and pattern bifurcations in a model for spatial patterns in young mussel beds

2008 ◽  
Vol 6 (37) ◽  
pp. 705-718 ◽  
Author(s):  
Rong-Hua Wang ◽  
Quan-Xing Liu ◽  
Gui-Quan Sun ◽  
Zhen Jin ◽  
Johan van de Koppel
Keyword(s):  
Spatial Patterns ◽  
Large Scale ◽  
Flow Instability ◽  
Reaction Diffusion ◽  
Movement Speed ◽  
Model Parameters ◽  
Mussel Beds ◽  
Differential Flow ◽  
Wide Range ◽  
Numerical Bifurcation

Young mussel beds on soft sediments can display large-scale regular spatial patterns. This phenomenon can be explained relatively simply by a reaction–diffusion–advection (RDA) model of the interaction between algae and mussel, which includes the diffusive spread of mussel and the advection of algae. We present a detailed analysis of pattern formation in this RDA model. We derived the conditions for differential-flow instability that cause the formation of spatial patterns, and then systematically investigated how these patterns depend on model parameters. We also present a detailed study of the patterned solutions in the full nonlinear model, using numerical bifurcation analysis of the ordinary differential equations, which were obtained from the RDA model. We show that spatial patterns occur for a wide range of algal concentrations, even when algal concentration is much lower than the prediction by linear analysis in the RDA model. That is to say, spatial patterns result from the interaction of nonlinear terms. Moreover, patterns with different wavelength, amplitude and movement speed may coexist. The results obtained are consistent with the previous observation that self-organization allows mussels to persist with algal concentrations that would not permit survival of mussels in a homogeneous bed.

Differential Flow Instability in Tubular Flow Reactor:  Its Convective Nature

1996 ◽  
Vol 100 (39) ◽  
pp. 15810-15814 ◽  
Author(s):  
Xiao-Guang Wu ◽  
Satoshi Nakata ◽  
Michael Menzinger ◽  
Arkady Rovinsky
Keyword(s):  
Flow Reactor ◽  
Flow Instability ◽  
Differential Flow ◽  
Tubular Flow Reactor ◽  
Tubular Flow
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