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These are solved in a numerical continuation package, such that the response far into the unstable range can be portrayed.
For our numerical investigations, we used the continuation package Auto[55, 56] for solving the boundary value problems.
Using the continuation package AUTO [7], and closely following the techniques outlined in [5], the nonsingular canard, Ξ t, is found for τ s = 15 and is then continued in τ s.
For more extensive computation of H′(0) as a function of parameters P and Q, an in-house interface to the Matlab-based continuation package MATCONT (http://www.matcont.ugent.be/) was used.
Matcont, a Matlab continuation package with a graphic user interface (GUI) for interactive numerical study of parameterized nonlinear ordinary differential equations (ODEs), computes curves of equilibria, limit points, Hopf point, limit cycles, fold, torus, and branch point bifurcation of limit cycles [ 91].
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In this paper, we use various 2PBVP formulations to compute slow manifolds and their stable and unstable manifolds, as well as canard orbits; the respective families of solutions are found with the continuation software package AUTO [62].
Because of that bifurcations of stiff bursting solutions, especially irregular ones, are hard to trace down by parameter continuation software packages such as CONTENT and AUTO-based packages, which are specifically designed mainly for explorations of equilibria and 'typical' periodic orbits.
AUTO_DAE is based on the open source continuation and bifurcation computational package AUTO (Doedel et al., 1997), thoroughly used to investigate the behavior of ODEs.
These services can be in addition to traditional services packages or continuation of benefits.
The calculation of bifurcations can be performed through continuation softwares, like the MatCont package [ 40], which we have used to perform the analysis illustrated in Figures 5 and 6.
By John Cassidy August 20, 2015 Alexis Tsipras's resignation is probably a smart move, and it will also give the Greek public an opportunity to register their feelings, once again, about the bailout package and its attendant continuation of austerity policies.
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