U. Parlitz and W. Lauterborn. Period-doubling cascades and devil's staircases of the driven van der pol equation. Physical Review A, 36(3):1428-- 1434, 1987. Home/Search Document Not in Database Summary Related Articles Check |
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Robust Adaptive Control Of Passive Systems With.. - Loria, Panteley.. (Correct)
....= q L C we obtain the well known equation v (1 Gamma v 2 ) v v = q cos( t) 26) which van der Pol used to model an electrical circuit with a triode valve. Note that for the particular case when = 5, q = 5 and = 2:463 the van der Pol oscillator exhibits a chaotic behaviour [14]. Consider now the controlled unperturbed van der Pol equation with the voltage v delivered to the active load as the output to be controlled, that is v (1 Gamma v 2 ) v v = u w; 27) where w is a bounded external input which includes the term q cos( t) and u (v) Gammak p v ....
U. Parlitz and W. Lauterborn. Period-doubling cascades and devil's staircases of the driven van der pol equation. Physical Review A, 36(3):1428-- 1434, 1987.
Pitch Perception of Complex Sounds: Nonlinearity.. - Gonzalez, Morettini.. (1995) (Correct)
....(where 1=1 stands for the frequency ratio) More complicated cases arise for an arbitrary rational frequency ratio. A beautiful example in nature is the 3=2 ratio between the orbital and rotation periods of the planet Mercury. A typical forced oscillator, such as the forced van der Pol oscillator [13], shows an infinity of these phase locked solutions depending on the values of the frequency and amplitude of the external force. For a constant value of the amplitude, the effective frequency ratio varies in a complicated manner with the external frequency, describing a kind of non differentiable ....
....which characterize them. We say that two rationals p=q and r=s are adjacents, if jq:r Gamma p:sj = 1: 1) Between adjacents we can define a Farey sum operation as follows p q Phi r s = p r q s : 2) Figure 3: Devil s staircase for the forced van der Pol oscillator (from ref. [13]) Every rational plateau corresponds to a phase locked solution, the denominator being the period of the response measured in periods of the external force. The rational obtained is called the mediant of the two adjacents. The mediant gives the local hierarchy of the widths of the plateaux, ....
U. Parlitz and W. Lauterborn, "Period-doubling cascades and devil's staircases of the driven van der Pol oscillator", Phys. Rev. A, vol. 36, pp. 1428-1434, 1987.
Nonlinear Dynamics in Modeling Cardiac Arrhythmias - Kongas (1998) (Correct)
....other types of solutions such as quasiperiodic, the LLE is zero. The behavior and computation of the LLE are treated in many papers (see Wolf et al. 1985, and references therein) Torsion of the flow around a periodic orbit is characterized by a torsion number (Aizawa and Uezu, 1982; Uezu, 1983; Parlitz and Lauterborn, 1986, 1987). The torsion number equals the number of turns of the infinitesimal difference vector around the periodic orbit during one period. For periodically driven 1 dof systems, Parlitz and Lauterborn (1986) introduced a generalized winding number (GWN) to characterize the torsion of the flow around the ....
U. Parlitz and W. Lauterborn. Period-doubling cascades and devil's staircases of the driven van der Pol oscillator. Phys. Rev., 36A(3):1428--1434, 1987.
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