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Chaos in a fractional order modified Duffing system. (English) Zbl 1132.37324
Summary: The chaotic behaviors in a fractional order modified Duffing system are studied numerically by phase portraits, Poincaré maps and bifurcation diagrams. Linear transfer function approximations of the fractional integrator block are calculated for a set of fractional orders in (0, 1], based on frequency domain arguments. The total system orders found for chaos to exist in such systems are 1.8, 1.9, 2.0, and 2.1.

37N05Dynamical systems in classical and celestial mechanics
70K55Transition to stochasticity (chaotic behavior)
26A33Fractional derivatives and integrals (real functions)
37G99Local and nonlocal bifurcation theory
37D45Strange attractors, chaotic dynamics
Full Text: DOI
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