Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present the GLOBALIZEBVP algorithm for the computation of two-dimensional stable and unstable manifolds of a vector field. Specifically,  use the collocation routines of AUTO to solve boundary problems that are used during the computation to find the next approximate geodesic level set on the manifold. The resulting implementation is numerically very stable and ll suited for systems with multiple time scales. This is illustrated with the test-case examples of the Lorenz and Chua systems, and with a slow–fast model of a somatotroph cell.
['James P. England', 'Bernd Krauskopf', 'Hinke M. Osinga']
I am writing a research paper on a idea Computing two-dimensional global invariant manifolds in slow-fast systems
[{"from": "human", "value": "I am writing a research paper on a idea Computing two-dimensional global invariant manifolds in slow-fast systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present the GLOBALIZEBVP algorithm for the computation of two-dimensional stable and unstable manifolds of a vector field. Specifically,  use the collocation routines of AUTO to solve boundary problems that are used during the computation to find the next approximate geodesic level set on the manifold. The resulting implementation is numerically very stable and ll suited for systems with multiple time scales. This is illustrated with the test-case examples of the Lorenz and Chua systems, and with a slow\u2013fast model of a somatotroph cell."}]