108 citations · 512 across the 23 of their papers we have counts for
12 papers · 1 filter
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…
Homoclinic chaos and its organization in a nonlinear optics model
Krishna Pusuluri, Andrey L Shilnikov
We developed a powerful computational approach to elaborate on onset mechanisms of deterministic chaos due to complex homoclinic bifurcations in diverse systems. Its core is the re…
Unraveling the Chaos-land and its organization in the Rabinovich System
Krishna Pusuluri, Arkady Pikovsky, Andrey Shilnikov
A suite of analytical and computational techniques based on symbolic representations of simple and complex dynamics, is further developed and employed to unravel the global organiz…
Bottom-up approach to torus bifurcation in neuron models
Huiwen Ju, Alexander Neiman, Andrey Shilnikov
We study the quasi-periodicity phenomena occurring at the transition between tonic spiking and bursting activities in exemplary biologically plausible Hodgkin-Huxley type models of…
Qualitative and Quantitative Stability Analysis of Penta-rhythmic Circuits
Justus T. C. Schwabedal, Drake E. Knapper, A. L. Shilnikov
Inhibitory circuits of relaxation oscillators are often-used models for the dynamics of biological networks. We present a qualitative and quantitative stability analysis of such a…
Mixed mode synchronization and network bursting of neurons with post-inhibitory rebound
Roman Nagornov, Grigory Osipov, Maxim Komarov +2
This study is focused on the mechanisms of rhythmogenesis and robustness of anti-phase bursting in half-center-oscillators (HCOs) consisting of two reciprocally inhibitory coupled…