Multistability in a system of two coupled oscillators with delayed feedback. (English) Zbl 1410.34200
The author considers an infinite-dimensional dynamical system associated to two weakly coupled oscillators with nonlinear compactly supported delayed feedback. In fact, he studies a family of such systems depending on a large parameter. In order to study the existence and stability of relaxation periodic orbits of this dynamical system, the author is able to construct a finite dimensional mapping and to prove that the initial problem is equivalent to study the dynamics of this mapping. Asymptotic formulas of these relaxation periodic solutions were constructed.
Reviewer: Adriana Buică (Cluj-Napoca)
MSC:
| 34K13 | Periodic solutions to functional-differential equations |
| 34K25 | Asymptotic theory of functional-differential equations |
| 34K26 | Singular perturbations of functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
Keywords:
delay; large parameter; relaxation oscillation; nonlocal dynamics; periodic solution; asymptoticsReferences:
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