108 citations · 512 across the 23 of their papers we have counts for
25 papers
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…
Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits
James Scully, Jassem Bourahmah, David Bloom +1
The purpose of this paper is trifold -- to serve as an instructive resource and a reference catalog for biologically plausible modeling with i) conductance-based models, coupled wi…
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…
Homoclinic chaos in the Rössler model
Semyon Malykh, Yuliya Bakhanov, Alexey Kazakov +2
We study the origin of homoclinic chaos in the classical 3D model proposed by O. Rössler in 1976. Of our particular interest are the convoluted bifurcations of the Shilnikov saddle…