Travelling waves in the Nicholson’s blowflies equation with spatio-temporal delay

2009 ◽  
Vol 209 (2) ◽  
pp. 314-326 ◽  
Author(s):  
Guojian Lin
Keyword(s):  
Travelling Waves ◽  
Temporal Delay ◽  
Nicholson’S Blowflies Equation ◽  
Spatio Temporal

Spatio-temporal regimes in Rayleigh–Bénard convection in a small rectangular cell

1989 ◽  
Vol 209 ◽  
pp. 309-334 ◽  
Author(s):  
M. A. Rubio ◽  
P. Bigazzi ◽  
L. Albavetti ◽  
S. Ciliberto
Keyword(s):  
Travelling Waves ◽  
Rectangular Cell ◽  
Complex Behaviour ◽  
Temporal Behaviour ◽  
Bénard Convection ◽  
Benard Convection ◽  
Spatio Temporal ◽  
Roll Axis ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

By means of an original optical technique we have studied the spatio-temporal behaviour in a Rayleigh–Bénard convection experiment of small rectangular geometry. The experimental technique allows complete reconstruction of the temperature field integrated along the roll axis. Two main spatiotemporal regimes have been found, corresponding to localized oscillations and travelling waves respectively. Several parameters are proposed for the quantitative characterization of this complex behaviour.

scholarly journals Spatially mismatched trophic dynamics: cyclically outbreaking geometrids and their larval parasitoids

2010 ◽  
Vol 6 (4) ◽  
pp. 566-569 ◽  
Author(s):  
Snorre B. Hagen ◽  
Jane U. Jepsen ◽  
Tino Schott ◽  
Rolf A. Ims
Keyword(s):  
Trophic Interactions ◽  
Travelling Waves ◽  
Methodological Approach ◽  
Spatial Dynamics ◽  
Population Cycles ◽  
Trophic Levels ◽  
Trophic Dynamics ◽  
Spatial Mismatch ◽  
Larval Parasitoids ◽  
Spatio Temporal

For trophic interactions to generate population cycles and complex spatio-temporal patterns, like travelling waves, the spatial dynamics must be matched across trophic levels. Here, we propose a spatial methodological approach for detecting such spatial match–mismatch and apply it to geometrid moths and their larval parasitoids in northern Norway, where outbreak cycles and travelling waves occur. We found clear evidence of spatial mismatch, suggesting that the spatially patterned moth cycles in this system are probably ruled by trophic interactions involving other agents than larval parasitoids.

Noise-induced suppression of periodic travelling waves in oscillatory reaction–diffusion systems

2010 ◽  
Vol 466 (2119) ◽  
pp. 1903-1917 ◽  
Author(s):  
Michael Sieber ◽  
Horst Malchow ◽  
Sergei V. Petrovskii
Keyword(s):  
Travelling Waves ◽  
Natural Populations ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Oscillatory Reaction ◽  
Stochastic Forcing ◽  
Spatial Direction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Spatio Temporal

Ecological field data suggest that some species show periodic changes in abundance over time and in a specific spatial direction. Periodic travelling waves as solutions to reaction–diffusion equations have helped to identify possible scenarios, by which such spatio-temporal patterns may arise. In this paper, such solutions are tested for their robustness against an irregular temporal forcing, since most natural populations can be expected to be subject to erratic fluctuations imposed by the environment. It is found that small environmental noise is able to suppress periodic travelling waves in stochastic variants of oscillatory reaction–diffusion systems. Irregular spatio-temporal oscillations, however, appear to be more robust and persist under the same stochastic forcing.

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