Analysing periodicity, nonlinearity and transitional characteristics of nonlinear dynamic systems with periodicity ratio (PR)

DOI10.1016/j.cnsns.2011.05.037zbMath1234.34028OpenAlexW2007602321MaRDI QIDQ654341

Lu Han, Liming Dai

Publication date: 28 December 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2011.05.037

zbMATH Keywords

nonlinear dynamic systemsLyapunov exponentconvergent timediagnosis of nonlinear behaviourDuffing's systemsmultiple-periodicityperiodicity ratiotransitional characteristics

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Complex behavior and chaotic systems of ordinary differential equations (34C28)

Related Items (1)

An algorithm for diagnosing nonlinear characteristics of dynamic systems with the integrated periodicity ratio and Lyapunov exponent methods

Cites Work

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• A qualitative study of the damped Duffing equation and applications
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
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• A. M. Lyapunov's stability theory—100 years on
• Nonlinear Dynamics of Piecewise Constant Systems and Implementation of Piecewise Constant Arguments
• Bifurcation and stability of periodic solutions of Duffing equations
• The bifurcations of duffing's equation: An application of catastrophe theory
• Transition to chaos for random dynamical systems

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