Deterministic Systems with Random Initial Conditions

1992 ◽  
pp. 25-62
Author(s):  
N. Bellomo ◽  
Z. Brzezniak ◽  
L. M. de Socio
Keyword(s):  
Initial Conditions ◽  
Deterministic Systems ◽  
Random Initial Conditions

scholarly journals Burgers' turbulence problem with linear or quadratic external potential

2005 ◽  
Vol 42 (02) ◽  
pp. 550-565 ◽  
Author(s):  
O. E. Barndorff-Nielsen ◽  
N. N. Leonenko
Keyword(s):  
Burgers Equation ◽  
Initial Conditions ◽  
External Potential ◽  
Limit Laws ◽  
Random Initial Conditions ◽  
Burgers Turbulence

We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.

scholarly journals Chimera States in Star Networks

2016 ◽  
Vol 26 (09) ◽  
pp. 1630023 ◽  
Author(s):  
Chandrakala Meena ◽  
K. Murali ◽  
Sudeshna Sinha
Keyword(s):  
Analog Circuit ◽  
Initial Conditions ◽  
Mean Field ◽  
Coupled Systems ◽  
Dynamical Equations ◽  
Chimera States ◽  
Diffusive Coupling ◽  
Star Networks ◽  
Random Initial Conditions ◽  
Coupling Strengths

We consider star networks of chaotic oscillators, with all end-nodes connected only to the central hub node, under diffusive coupling, conjugate coupling and mean-field diffusive coupling. We observe the existence of chimeras in the end-nodes, which are identical in terms of the coupling environment and dynamical equations. Namely, the symmetry of the end-nodes is broken and coexisting groups with different synchronization features and attractor geometries emerge. Surprisingly, such chimera states are very wide-spread in this network topology, and large parameter regimes of moderate coupling strengths evolve to chimera states from generic random initial conditions. Further, we verify the robustness of these chimera states in analog circuit experiments. Thus it is evident that star networks provide a promising class of coupled systems, in natural or engineered contexts, where chimeras are prevalent.

scholarly journals Advancing from Convection-Allowing NWP to Warn-on-Forecast: Evidence of Progress

2018 ◽  
Vol 33 (2) ◽  
pp. 599-607 ◽  
Author(s):  
John R. Lawson ◽  
John S. Kain ◽  
Nusrat Yussouf ◽  
David C. Dowell ◽  
Dustan M. Wheatley ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Real Time ◽  
Initial Conditions ◽  
Spatial Scales ◽  
Weather Prediction ◽  
Radar Data ◽  
Model Systems ◽  
Deterministic Systems ◽  
Forecast Lead Time ◽  
The Impact

Abstract The Warn-on-Forecast (WoF) program, driven by advanced data assimilation and ensemble design of numerical weather prediction (NWP) systems, seeks to advance 0–3-h NWP to aid National Weather Service warnings for thunderstorm-induced hazards. An early prototype of the WoF prediction system is the National Severe Storms Laboratory (NSSL) Experimental WoF System for ensembles (NEWSe), which comprises 36 ensemble members with varied initial conditions and parameterization suites. In the present study, real-time 3-h quantitative precipitation forecasts (QPFs) during spring 2016 from NEWSe members are compared against those from two real-time deterministic systems: the operational High Resolution Rapid Refresh (HRRR, version 1) and an upgraded, experimental configuration of the HRRR. All three model systems were run at 3-km horizontal grid spacing and differ in initialization, particularly in the radar data assimilation methods. It is the impact of this difference that is evaluated herein using both traditional and scale-aware verification schemes. NEWSe, evaluated deterministically for each member, shows marked improvement over the two HRRR versions for 0–3-h QPFs, especially at higher thresholds and smaller spatial scales. This improvement diminishes with forecast lead time. The experimental HRRR model, which became operational as HRRR version 2 in August 2016, also provides added skill over HRRR version 1.

scholarly journals Sources of uncertainty in deterministic dynamics: an informal overview

2011 ◽  
Vol 369 (1956) ◽  
pp. 4705-4729 ◽  
Author(s):  
Ian Stewart
Keyword(s):  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Sources Of Uncertainty ◽  
Deterministic Systems ◽  
Coin Tossing ◽  
Random Switching ◽  
Butterfly Effect ◽  
Basin Boundaries ◽  
Sensitivity To Initial Conditions

The discovery of chaotic dynamics implies that deterministic systems may not be predictable in any meaningful sense. The best-known source of unpredictability is sensitivity to initial conditions (popularly known as the butterfly effect), in which small errors or disturbances grow exponentially. However, there are many other sources of uncertainty in nonlinear dynamics. We provide an informal overview of some of these, with an emphasis on the underlying geometry in phase space. The main topics are the butterfly effect, uncertainty in initial conditions in non-chaotic systems, such as coin tossing, heteroclinic connections leading to apparently random switching between states, topological complexity of basin boundaries, bifurcations (popularly known as tipping points) and collisions of chaotic attractors. We briefly discuss possible ways to detect, exploit or mitigate these effects. The paper is intended for non-specialists.

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