On the existence and stability of a two-dimensional relaxational torus
Copyright policy )On the existence and stability of a two-dimensional relaxational torus
The theory of relaxational oscillations for systems of ordinary differential equations with a small parameter at some derivatives has been currently developed sufficiently well to consider different applications. In particular, in the case of three-dimensional systems with one slow variable, the problem stated in the title of this paper was solved by the author and \textit{E. F. Mischenko} [Russ. Math. Surv. 44, No. 3, 204-205 (1989); translation from Usp. Mat. Nauk 44, No. 3 (267), 161- 162 (1989; Zbl 0704.34003)]. We now study this problem in the more complicated case of two slow variables. We also describe special mechanisms which lead to destruction of the relaxational torus.
relaxational torus, Singular perturbations for ordinary differential equations, relaxational oscillations, Nonlinear oscillations and coupled oscillators for ordinary differential equations, Manifolds of solutions of ODE, ordinary differential equations with a small parameter at some derivatives, two slow variables
relaxational torus, Singular perturbations for ordinary differential equations, relaxational oscillations, Nonlinear oscillations and coupled oscillators for ordinary differential equations, Manifolds of solutions of ODE, ordinary differential equations with a small parameter at some derivatives, two slow variables
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