Optimization analysis of Duffing oscillator with fractional derivatives

DOI10.1007/s11071-014-1744-zzbMath1345.49044OpenAlexW1976165933MaRDI QIDQ493956

Haitao Liao

Publication date: 7 September 2015

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-014-1744-z

zbMATH Keywords

stabilityuncertaintyinterval analysisperiodic solutionharmonic balance methodfractional derivative

Mathematics Subject Classification ID

Control/observation systems with incomplete information (93C41) Stability for nonlinear problems in mechanics (70K20) Equilibria and periodic trajectories for nonlinear problems in mechanics (70K42) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Simulation of dynamical systems (37M05) Dynamical systems in classical and celestial mechanics (37N05) Fractional ordinary differential equations (34A08) Problems with incomplete information (optimization) (49N30)

Related Items (7)

Efficient sensitivity analysis method for chaotic dynamical systems ⋮ EFFECT OF FRACTIONAL DERIVATIVE PROPERTIES ON THE PERIODIC SOLUTION OF THE NONLINEAR OSCILLATIONS ⋮ Three classes of fractional oscillators ⋮ Stochastic resonance for a fractional linear oscillator with two-kinds of fractional-order derivatives subject to multiplicative and signal-modulated noise ⋮ Synchronization of Fractional Chaotic and Hyperchaotic Systems Using an Extended Active Control ⋮ Dynamics of Fractional Order Complex Uçar System ⋮ A single variable-based method for concurrent multiscale topology optimization with multiple materials

Uses Software

• sysdfod
• DFOC

Cites Work

• Unnamed Item
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• A harmonic-based method for computing the stability of periodic solutions of dynamical systems
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• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Computation of fractional derivatives using Fourier transform and digital FIR differentiator.
• Stochastic study of a non-linear self-excited system with friction
• Approximate expressions of a fractional order Van der Pol oscillator by the residue harmonic balance method
• Fractional derivative and time delay damper characteristics in Duffing-van der Pol oscillators
• Dynamic behavior of fractional order duffing chaotic system and its synchronization via singly active control
• Parameter perturbation method for dynamic responses of structures with uncertain-but-bounded parameters based on interval analysis

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