108 citations · 512 across the 23 of their papers we have counts for
5 papers · 1 filter
Bifurcation structure of interval maps with orbits homoclinic to a saddle-focus
Carter Hinsley, James Scully, Andrey L. Shilnikov
We study homoclinic bifurcations in an interval map associated with a saddle-focus of (2, 1)-type in -symmetric systems. Our study of this map reveals the homoclinic…
Leonid Shilnikov and mathematical theory of dynamical chaos
Alexey Kazakov, Sergey Gonchenko, Dmitry Turaev +1
This Focus Issue Global Bifurcations, Chaos, and Hyperchaos Theory and Applications is dedicated to the 85th anniversary of the great mathematician, one of the founding fathers of…
Measuring chaos in the Lorenz and Rössler models: Fidelity tests for reservoir computing
James Scully, Alexander Neiman, Andrey Shilnikov
This study is focused on the qualitative and quantitative characterization of chaotic systems with the use of symbolic description. We consider two famous systems: Lorenz and Rössl…
Ordered intricacy of Shilnikov saddle-focus homoclinics in symmetric systems
Tingli Xing, Krishna Pusuluri, Andrey L. Shilnikov
Using the technique of Poincaré return maps, we disclose an intricate order of the subsequent homoclinics near the primary homoclinic bifurcation of the Shilnikov saddle-focus in s…
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…