A general numerical technique is proposed for the assessment of the stability of periodic solutions and the determination of bifurcations for limit cycles in autonomous nonlinear systems represented by ordinary differential equations in the differential-algebraic form. The method is based on the harmonic balance technique, and exploits the same Jacobian matrix of the nonlinear system used in the Newton iterative numerical solution of the harmonic balance equations for the determination of the periodic steady-state. To demonstrate the approach, it is applied to the determination of the bifurcation curves in the parameters' space of Chua's circuit with cubic nonlinearity, and to study the dynamics of the limit cycle of a Colpitts oscillator.

A frequency-domain approach to the analysis of stability and bifurcations in nonlinear systems described by differential-algebraic equations / Traversa, F. L.; Bonani, Fabrizio; DONATI GUERRIERI, Simona. - In: INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS. - ISSN 0098-9886. - STAMPA. - 36:4(2008), pp. 421-439. [10.1002/CTA.440]

A frequency-domain approach to the analysis of stability and bifurcations in nonlinear systems described by differential-algebraic equations

BONANI, Fabrizio;DONATI GUERRIERI, Simona
2008

Abstract

A general numerical technique is proposed for the assessment of the stability of periodic solutions and the determination of bifurcations for limit cycles in autonomous nonlinear systems represented by ordinary differential equations in the differential-algebraic form. The method is based on the harmonic balance technique, and exploits the same Jacobian matrix of the nonlinear system used in the Newton iterative numerical solution of the harmonic balance equations for the determination of the periodic steady-state. To demonstrate the approach, it is applied to the determination of the bifurcation curves in the parameters' space of Chua's circuit with cubic nonlinearity, and to study the dynamics of the limit cycle of a Colpitts oscillator.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1641004
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