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Kuznecov A. P., Kuznecov S. P., Stankevich N. V. Four-dimensional system with torus attractor birth via saddle-node bifurcation of limit cycles in context of family of blue sky catastrophes. Izvestiya VUZ. Applied Nonlinear Dynamics, 2015, vol. 23, iss. 4, pp. 32-39. DOI:


Four-dimensional system with torus attractor birth via saddle-node bifurcation of limit cycles in context of family of blue sky catastrophes

Kuznecov Aleksandr Petrovich, Saratov State University
Kuznecov Sergej Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Stankevich Natalija Vladimirovna, Yuri Gagarin State Technical University of Saratov

A new four-dimensional model with quasi-periodic dynamics is suggested. The torus attractor originates via the saddle-node bifurcation, which may be regarded as a member of a bifurcation family embracing different types of blue sky catastrophes. Also the torus birth through the Neimark-Sacker bifurcation occurs in some other region of the parameter space.   Download full version


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