Figure 1: This animation shows the evolution of two points lying on the same isochron. 1-dimensional sets of points with the same asymptotic phase. Since the vector field is symmetric under rotations around the origin, the family of isochrons must be invariant under that symmetry. The constant is set to -1 pavlidis biological oscillators forex that the value of the asymptotic phase agrees with the angular coordinate on the limit cycle.
In this example isochrons are defined everywhere in the plane, except at the origin, which is the only element of the phaseless set. This illustrates how the asymptotic phase can be used to find a change of coordinates in which the dynamics of the phase coordinate is decoupled from the remaining coordinates. Isochrons have found a number of applications. As noted in the previous example, they can be used to effectively reduce the dimension of the equation in the neighborhood of a periodic orbit. Extending the notion of phase of a periodic orbit to a neighborhood of the periodic orbit. Deterministic chaos and stochastic dynamics can show a rhythmic component, and such types of irregular oscillations have been described by phase models. Without a periodic orbit, the standard definition of phase via isochrones is however not applicable.
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Normally Hyperbolic Invariant Manifolds in Dynamical Systems. Jeff Moehlis, Kresimir Josic, Eric T. Your list has reached the maximum number of items. Your request to send this item has been completed.
Cancel Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study. You may send this item to up to five recipients. 843199169 Title: Biological Oscillators : Their Mathematical Analysis. Author: Theodosios Pavlidis Publisher: Oxford : Elsevier Science, 1973.
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