Influence of random initial conditions on the evolution of nonlinear systems

1987 ◽  
Vol 146 (3) ◽  
pp. 650-656 ◽  
Author(s):  
M. Frankowicz ◽  
M.Malek Mansour ◽  
F. Baras
Keyword(s):  
Nonlinear Systems ◽  
Initial Conditions ◽  
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.

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