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The parameter functionalization method for the problem of saddle-node bifurcations in dynamical systems

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We propose new sufficient conditions for saddle-node bifurcations in one- and twoparametric dynamical systems obtained with the parameter functionalization method, derive asymptotic formulas for the resulting solutions, and analyze their stability. As an application, we consider the synchronization problem for periodic oscillations of an autonomous Van der Pol generator under an external harmonic influence.

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Correspondence to M. G. Yumagulov.

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Original Russian Text © M.G. Yumagulov, E.S. Imangulova, 2017, published in Avtomatika i Telemekhanika, 2017, No. 4, pp. 63–77.

This paper was recommended for publication by A.M. Krasnosel’skii, a member of the Editorial Board

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Yumagulov, M.G., Imangulova, E.S. The parameter functionalization method for the problem of saddle-node bifurcations in dynamical systems. Autom Remote Control 78, 630–642 (2017).

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