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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.

MSC:
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
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References:
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