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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:

37N05 Dynamical systems in classical and celestial mechanics
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
26A33 Fractional derivatives and integrals
37G99 Local and nonlocal bifurcation theory for dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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