Periodically-forced finite networks of heterogeneous globally-coupled oscillators: A low-dimensional approach

2008 ◽  
Vol 237 (2) ◽  
pp. 207-215 ◽  
Author(s):  
Carlo R. Laing ◽  
Ioannis G. Kevrekidis
Keyword(s):  
Coupled Oscillators ◽  
Dimensional Approach ◽  
Low Dimensional

A low-dimensional approach to closed-loop control of a Mach 0.6 jet

2013 ◽  
Vol 54 (4) ◽  
Author(s):  
Kerwin R. Low ◽  
Zachary P. Berger ◽  
Stanislav Kostka ◽  
Basman ElHadidi ◽  
Sivaram Gogineni ◽  
...  
Keyword(s):  
Closed Loop ◽  
Closed Loop Control ◽  
Dimensional Approach ◽  
Loop Control ◽  
Low Dimensional

scholarly journals EFFICIENT INTEGRATION OF THE VARIATIONAL EQUATIONS OF MULTIDIMENSIONAL HAMILTONIAN SYSTEMS: APPLICATION TO THE FERMI–PASTA–ULAM LATTICE

2012 ◽  
Vol 22 (09) ◽  
pp. 1250216 ◽  
Author(s):  
ENRICO GERLACH ◽  
SIEGFRIED EGGL ◽  
CHARALAMPOS SKOKOS
Keyword(s):  
Hamiltonian Systems ◽  
Coupled Oscillators ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Variational Equations ◽  
Integration Schemes ◽  
Chaos Detection ◽  
Efficient Integration ◽  
Low Dimensional ◽  
Series Expansion Method

We study the problem of efficient integration of variational equations in multidimensional Hamiltonian systems. For this purpose, we consider a Runge–Kutta-type integrator, a Taylor series expansion method and the so-called "Tangent Map" (TM) technique based on symplectic integration schemes, and apply them to the Fermi–Pasta–Ulam β (FPU-β) lattice of N nonlinearly coupled oscillators, with N ranging from 4 to 20. The fast and accurate reproduction of well-known behaviors of the Generalized Alignment Index (GALI) chaos detection technique is used as an indicator for the efficiency of the tested integration schemes. Implementing the TM technique — which shows the best performance among the tested algorithms — and exploiting the advantages of the GALI method, we successfully trace the location of low-dimensional tori.

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