Geodesic
On the stability of coupled nonlinear oscillators
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 196 (2021), pp. 44-49

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In this paper, we consider the problem of Yu. N. Bibikov on the stability of equilibrium positions of two coupled nonlinear oscillators under the action of conservative perturbing forces. We obtain stability and instability conditions for the case of sufficiently small perturbing forces. Also, we consider the problem of stabilizing an equilibrium position by potential forces when only the relative position of the oscillators is measured and propose the form of a stabilizing potential.
Keywords: nonlinear oscillator, Hamiltonian system with two degrees of freedom, stability, stabilization under incomplete measurement. 
@article{INTO_2021_196_a4,
     author = {A. A. Kosov},
     title = {On the stability of coupled nonlinear oscillators},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {44--49},
     publisher = {mathdoc},
     volume = {196},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_196_a4/}
}
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A. A. Kosov. On the stability of coupled nonlinear oscillators. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 196 (2021), pp. 44-49. http://geodesic.mathdoc.fr/item/INTO_2021_196_a4/