Shilnikov bifurcation
نویسندگان
چکیده
منابع مشابه
Shilnikov bifurcation: Stationary Quasi-Reversal bifurcation
A generic stationary instability that arise in quasi-reversible systems is studying, which is characterized by the confluence of three eigenvalues at the origin of complex plane with only one eigenfunction. We characterize the unified description of this bifurcation and the dynamics exhibits by this model. In particular, the chaotic behavior—homoclinic Shilnikov chaos—exhibits by this model. A ...
متن کاملThe Shilnikov Saddle-Node Bifurcation in a Monetary Policy with Endogenous Time Preference
We improve the analysis made in Chang et al (2011), by exploring the possibilities for the raise of global indeterminacy via a Shilnikov saddle-node bifurcation on an invariant circle. This allows us to better understand the determinants for the emergence of endogenous fluctuations in a monetary policy model, and to explain the existence of irregular patterns. Hence, the economy may start at so...
متن کاملDetecting the Shilnikov scenario in a Hopf-Hopf bifurcation with 1:3 resonance
We investigate the behaviour of the primary solutions at a Hopf-Hopf interaction close to a 1:3 resonance. It turns out, that the secondary bifurcations from the primary periodic solution branches are governed by Duffing and Mathieu equations. By numerical path following a homoclinic orbit at a saddle node was detected, giving rise to the Shilnikov scenario. In order to understand the creation ...
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The dynamics of an idealized wind-driven double-gyre circulation in an ocean basin are studied from a dynamical systems point of view in an effort to better understand its variability. While previous analyses of this circulation have mostly dealt with local bifurcations of steady states and limit cycles, this study demonstrates the importance of considering global bifurcations as well. In one c...
متن کاملEditorial - Leonid Pavlovich Shilnikov
This special issue presents a selection of papers from the conference “Dynamics, Bifurcations and Strange Attractors” dedicated to the memory of Leonid Pavlovich Shilnikov (1934–2011) to commemorate his contributions to the theory of dynamical systems and bifurcations. The conference was held at the Lobachevsky State University of Nizhny Novgorod, Russia, on 1–5 July 2013. The conference was at...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2007
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.1891