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ISSN 2542-1905 (Online)

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Zhusubaliev Z. T., Janochkina O. O. Bifurcations of a two-­dimensional torus in piecewise-­smooth dynamical systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 6, pp. 86-98. DOI: 10.18500/0869-6632-2009-17-6-86-98

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Bifurcations of a two-­dimensional torus in piecewise-­smooth dynamical systems

Zhusubaliev Zhanybaj Tursunbaevich, Federal state budgetary educational institution of higher professional education "South-West state University"
Janochkina Olga Olegovna, Federal state budgetary educational institution of higher professional education "South-West state University"

Considering a set of coupled nonautonomous differential equations with discontinuous right-hand sides, we discuss two different scenarios for torus birth bifurcations in piecewise-smooth dynamical systems. One scenario is the continuous transformation of the stable equilibrium into an unstable focus period-1 orbit surrounded by a resonant or ergodic torus. Another is the transition from a stable periodic orbit to an invariant torus through a border-collision bifurcation in which two complex-conjugate multipliers jump abruptly from the inside to the outside of the unit circle.

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