Complex dynamics and bifurcations in a Hamiltonian system having a transversal homoclinic orbit to a saddle focus
Related Experiment Video
Updated: Sep 25, 2026

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
Published on: February 3, 2014
1Research Institute for Applied Mathematics & Cybernetics, 603005 Nizhnii Novgorod, USSR.
Abstract:
A Hamiltonian system having a saddle-focus singular point with a transversal homoclinic orbit is considered. The bifurcations that occur upon a variation of the Hamiltonian are studied. Reconstructions of a symbolic system describing the hyperbolic set are investigated. Bifurcations linked with the appearance of Smale horseshoes are pointed out. The results are applied to a system determining traveling-wave solutions of the Landau-Lifshitz equation. Multisolitons with any number of humps can exist.
More Related Videos
Related Concept Videos
Root Loci for Positive-Feedback Systems
The construction rules for the root locus in positive feedback systems are similar to those in...
Pole and System Stability
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Euler Equations of Motion
Transmission-Line Differential Equations
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Stability
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Euler's Equations of Motion

