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math.DS2026
On a stable torus in a 3D system with a saddle-focus
Andrey L. Shilnikov answered Leonid P. Shilnikov
This paper proposes a conceptual model for the onset of a stable torus near a saddle-focus equilibrium. This bifurcation scenario is typical of slow-fast systems that generate elli…
math.DS2013★ 24 cited
Showcase of Blue Sky Catastrophes
Leonid Shilnikov, Andrey Shilnikov, Dmitry Turaev
Let a system of differential equations possess a saddle-node periodic orbit such that every orbit in its unstable manifold is homoclinic, i.e. the unstable manifold is a subset of…
math.DS2003★ 34 cited
Bifurcations and strange attractors
Leonid Shilnikov
We review the theory of strange attractors and their bifurcations. All known strange attractors may be subdivided into the following three groups: hyperbolic, pseudo-hyperbolic one…