Global structural stability of a saddle node bifurcation
نویسندگان
چکیده
منابع مشابه
Constraint at a Saddle Node Bifurcation
Many power engineering systems have dynamic state variables which can encounter constraints or limits affecting system stability. Voltage collapse is an instability associated with the occurrence of a saddle node bifurcation in the equations which model the electric power system. We investigate the effect of constraints on voltage collapse by studying the effect of constraining state variables ...
متن کاملA double saddle-node bifurcation theorem
We consider an abstract equation F (λ, u) = 0 with one parameter λ, where F ∈ C(R × X,Y ), p ≥ 2 is a nonlinear differentiable mapping, and X,Y are Banach spaces. We apply Lyapunov-Schmidt procedure and Morse Lemma to obtain a “double” saddle-node bifurcation theorem near a degenerate point with a two-dimensional kernel. It is shown that the solution set of the equation is the union of two para...
متن کاملBifurcations of global reinjection orbits near a saddle-node Hopf bifurcation
The saddle-node Hopf bifurcation (SNH) is a generic codimensiontwo bifurcation of equilibria of vector fields in dimension at least three. It has been identified as an organizing centre in numerous vector field models arising in applications. We consider here the case that there is a global reinjection mechanism, because the centre manifold of the zero eigenvalue returns to a neighbourhood of t...
متن کاملA saddle-node bifurcation model of magnetic reconnection onset
It was recently shown that magnetic reconnection exhibits bistability, where the Sweet–Parker collisional and Hall collisionless reconnection solutions are both attainable for the same set of system parameters. Here, a dynamical model based on saddle-node bifurcations is presented which reproduces the slow to fast transition. It is argued that the properties of the dynamical model are a result ...
متن کاملExcitability in a Model with a Saddle-Node Homoclinic Bifurcation
In order to describe excitable reaction-diffusion systems, we derive a two-dimensional model with a Hopf and a semilocal saddle-node homoclinic bifurcation. This model gives the theoretical framework for the analysis of the saddle-node homoclinic bifurcation as observed in chemical experiments, and for the concepts of excitability and excitability threshold. We show that if diffusion drives an ...
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: Transactions of the American Mathematical Society
سال: 1978
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1978-0467832-8