Fractional standard map
Copyright policy )Fractional standard map
Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the parameter of the map and the fractional order of the derivative in the original differential equation this nonlinear dynamical system demonstrates attractors (fixed points, stables periodic trajectories, slow converging and slow diverging trajectories, ballistic trajectories, and fractal-like structures) and/or chaotic trajectories. At least one type of fractal-like sticky attractors in the chaotic sea was observed.
8 pages, 6 figures
- Yeshiva University United States
- Courant Institute of Mathematical Sciences New York University United States
- NEW YORK UNIVERSITY United States
- Lomonosov Moscow State University Russian Federation
- New York University United States
Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics, General perturbation schemes for nonlinear problems in mechanics, Perturbations of ordinary differential equations, FOS: Physical sciences, Perturbation theories for problems in Hamiltonian and Lagrangian mechanics, Fractional ordinary differential equations, Nonlinear Sciences - Chaotic Dynamics, Attractors of solutions to ordinary differential equations, attractor, fractional differential equation, discrete map, Chaotic Dynamics (nlin.CD)
Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics, General perturbation schemes for nonlinear problems in mechanics, Perturbations of ordinary differential equations, FOS: Physical sciences, Perturbation theories for problems in Hamiltonian and Lagrangian mechanics, Fractional ordinary differential equations, Nonlinear Sciences - Chaotic Dynamics, Attractors of solutions to ordinary differential equations, attractor, fractional differential equation, discrete map, Chaotic Dynamics (nlin.CD)
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