Codimension one and two bifurcations in a symmetrical ring network with delay
نویسندگان
چکیده
منابع مشابه
Blowout Bifurcations of Codimension Two
We consider examples of loss of stability of chaotic attractors in invariant subspaces (blowouts) that occur on varying two parameters, i.e. codimension two blowout bifurca-tions. Such bifurcations act as organising centres for nearby codimension one behaviour, analogous to the case for codimension two bifurcations of equilibria. We consider examples of blowout bifurcations showing change of cr...
متن کاملCodimension-Two Bifurcations in Animal Aggregation Models with Symmetry
Pattern formation in self-organised biological aggregation is a phenomenon that has been studied intensively over the past twenty years. In general, the studies on pattern formation focus mainly on identifying the biological mechanisms that generate these patterns. However, identifying the mathematical mechanisms behind these patterns is equally important, since it can offer information on the ...
متن کاملCodimension Two Bifurcations and Rythms in Neural Mass Models
Temporal lobe epilepsy is one of the most common chronic neurological disorder characterized by the occurrence of spontaneous recurrent seizures which can be observed at the level of populations through electroencephalogram (EEG) recordings. This paper summarizes some preliminary works aimed to understand from a theoretical viewpoint the occurrence of this type of seizures and the origin of the...
متن کاملNumerical Detection and Continuation of Saddle-node Homoclinic Bifurcations of Codimension One and Two
An extension of an existing truncated boundary-value method for the numerical continuation of connecting orbits is proposed to deal with homoclinic orbits to a saddle-node equilibrium. In contrast to previous numerical work by Schecter and Friedman & Doedel, the method is based on (linear) projection boundary conditions. These boundary conditions , with extra deening conditions for a saddle-nod...
متن کاملDynamical Systems with a Codimension-One Invariant Manifold: The Unfoldings and Its Bifurcations
We investigate dynamical system having a special structure namely a codimension-one invariant manifold that is preserved under the variation of parameters. We derive conditions such that bifurcations of codimension-one and of codimension-two occur in the system. The normal forms of these bifurcations are derived explicitly. Both local and global bifurcations are analysed and yield the transcrit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2015
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2014.12.067