Ordered intricacy of Shilnikov saddle-focus homoclinics in symmetric systems
arXiv:2104.11314 · doi:10.1063/5.0054776
Abstract
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 systems with reflection symmetry. We also reveal the admissible shapes of the corresponding bifurcation curves in a parameter plane of such systems. The scalability ratio of geometry and organization is proven to be universal for such homoclinic bifurcations of higher orders. Two applications with similar dynamics due to the Shilnikov saddle-foci, a smooth adaptation of the Chua circuit and a 3D normal form, are used to illustrate the theory
References in corpus (5)
- Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial
- Short-term synaptic plasticity in the deterministic Tsodyks-Markram model leads to unpredictable network dynamics
- Homoclinic puzzles and chaos in a nonlinear laser model
- Homoclinic chaos and its organization in a nonlinear optics model
- A phenomenological approach to normal form modeling: a case study in laser induced nematodynamics