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1. Hopf bifurcation for two types of Liénard systems

Author

Tian, Yun and Han, Maoan

Subjects
*BIFURCATION theory, *NUMBER theory, *LIMIT cycles, *MAXIMAL functions, *DIFFERENTIAL equations, *MATHEMATICAL analysis, *NUMERICAL analysis
Abstract

Abstract: In this paper we study the maximal number of limit cycles in Hopf bifurcations for two types of Liénard systems and obtain an upper bound of the number. In some cases the upper bound is the least, called the Hopf cyclicity. [Copyright &y& Elsevier]

Published
2011
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2. Asymptotic stability of forced oscillations emanating from a limit cycle

Author

Makarenkov, Oleg and Ortega, Rafael

Subjects
*OSCILLATION theory of differential equations, *LIMIT cycles, *ASYMPTOTIC theory of algebraic ideals, *DIFFERENTIAL equations, *PERIODIC functions, *BIFURCATION theory, *MATHEMATICAL analysis
Abstract

Abstract: Classical conditions for asymptotic stability of periodic solutions bifurcating from a limit cycle rely on the sign of the derivative of the associated bifurcation function at a zero. In this paper we show that, for analytic systems, this result is of topological nature. This means that it is enough to impose a change of sign at the zero, without any assumption on the succesive derivatives. [Copyright &y& Elsevier]

Published
2011
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