Synchronization of nonlinearly coupled harmonic oscillators

Cai, Chaohong
Tuna, Sezai Emre
Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the relative distance (between the states of the pair being coupled) vector. Under the assumption that the interconnection topology defines a connected graph, it is shown that the synchronization manifold is semiglobally practically asymptotically stable in the frequency of oscillations.
American Control Conference


Synchronization of linearly and nonlinearly coupled harmonic oscillators
Penbegül, Ali Yetkin; Tuna, Sezai Emre; Department of Electrical and Electronics Engineering (2011)
In this thesis, the synchronization in the arrays of identical and non-identical coupled harmonic oscillators is studied. Both linear and nonlinear coupling is considered. The study consists of two main parts. The first part concentrates on theoretical analysis and the second part contains the simulation results. The first part begins with introducing the harmonic oscillators and the basics of synchronization. Then some theoretical aspects of synchronization of linearly and nonlinearly coupled harmonic osci...
Synchronization analysis of coupled Lienard-type oscillators by averaging
Tuna, Sezai Emre (2012-08-01)
Sufficient conditions for the synchronization of coupled Lienard-type oscillators are investigated via averaging technique. The coupling considered here is fixed, nonsymmetric, and nonlinear. Under the assumption that the interconnection topology defines a connected graph, it is shown that the solutions of oscillators converge arbitrarily close to each other, starting from initial conditions arbitrarily far apart, provided that the frequency of oscillations is large enough and the initial phases of oscillat...
Synchronization of harmonic oscillators under restorative coupling with applications in electrical networks
Tuna, Sezai Emre (2017-01-01)
The role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied. Necessary and sufficient conditions, under which the individual systems' solutions converge to a common trajectory, are presented. Through simple physical examples, the meaning and limitations of the theorems are expounded. Also, to demonstrate their versatility, the results are extended to cover LTI passive electrical networks. One of the extensions generalizes the well-known link between the asymptoti...
Exact solution of the time-dependent harmonic plus an inverse harmonic potential with a time-dependent electromagnetic field
Yuce, C (2003-12-01)
In this paper, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic oscillator with time-independent parameters and the exact wave function is obtained.
Synchronization of small oscillations
Tuna, Sezai Emre (Elsevier BV, 2019-09-01)
Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative connectors. A construction is proposed to combine these two real matrices in a single complex matrix. It is shown that whether the oscillators synchronize in the steady state or not depend on the number of eigenvalues of this complex matrix on the imaginary axis. Certain refi...
Citation Formats
C. Cai and S. E. Tuna, “Synchronization of nonlinearly coupled harmonic oscillators,” presented at the American Control Conference, Baltimore, MD, 2010, Accessed: 00, 2020. [Online]. Available: