ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Zhusubaliev Z. T., Yanochkina 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

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
534.1
DOI: 
10.18500/0869-6632-2009-17-6-86-98

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

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

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.

Key words: 
Piecewise-smooth dynamical systems
border-collision bifurcation
invariant torus
equilibrium point
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Received: 
09.04.2009
Accepted: 
09.04.2009
Published: 
31.12.2009
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