Continuation of Connecting orbits in 3D-ODES (I): Point-to-Cycle Connections
نویسندگان
چکیده
This AUTO demo shows the use of a set of boundary conditions for the localization and continuation of the transcritical bifurcation of a limit cycle in a four-dimensional Marr-Pirt model.
منابع مشابه
Continuation of Connecting orbits in 3D-ODES (II) : Cycle-to-Cycle Connections
In Part I of this paper we discussed new methods for the numerical continuation of point-tocycle connecting orbits in 3-dimensional autonomous ODE’s using projection boundary conditions. In this second part we extend the method to the numerical continuation of cycle-to-cycle connecting orbits. In our approach, the projection boundary conditions near the cycles are formulated using eigenfunction...
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We propose new methods for the numerical continuation of point-to-cycle connecting orbits in 3-dimensional autonomous ODE's using projection boundary conditions. In our approach, the projection boundary conditions near the cycle are formulated using an eigenfunction of the associated adjoint variational equation, avoiding costly and numerically unstable computations of the monodromy matrix. The...
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A successive continuation method for locating connecting orbits in parametrized systems of autonomous ODEs was considered in [9]. In this paper we present an improved algorithm for locating and continuing connecting orbits, which includes a new algorithm for the continuation of invariant subspaces based on iterative re nement techniques.
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ورودعنوان ژورنال:
- I. J. Bifurcation and Chaos
دوره 18 شماره
صفحات -
تاریخ انتشار 2008