Localization of the Trajectory Bundles of Tunnel Type

Mathematical simulation of self-oscillations in methane oxidation on nickel: An isothermal model

“…A periodic solution with a period of 4.5 s was found by numerical integration of the Cauchy problem for system (1) with the initial data θ i (0) = 0 (i = 1, …, 10). The explicit third order Runge-Kutta method with a variable step size and local error estimation was used [42,43].…”

On estimation of the global error of numerical solution on canard-cycles

“…Trying to overcome the computational difficulties arising under numerical study of the maximal families of canardcycles in the case when the small parameter in the system does not approach zero, in [9] we proposed an analytical approach to estimate the localization of locally invariant manifolds which are O(µ) close to the critical manifold and generate a bundle of trajectories of the tunnel type. This method uses an envelope of the straight lines passing through the points of contact of the isoclines f 1 / f 2 = const with different slopes and the vector field.…”