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 کاملDynamics of Attention as Near Saddle-Node Bifurcation Behavior
In consideration of attention as a means for goal-directed behavior in non-stationary environments, we argue that the dynamics of attention should satisfy two opposing demands: long-term maintenance and quick transition. These two characteristics are contradictory within the linear domain. We propose the near saddlenode bifurcation behavior of a sigmoidal unit with self-connection as a candidat...
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 کاملPredicting Non-Stationary and Stochastic Activation of Saddle-Node Bifurcation
Accurately predicting the onset of large behavioral deviations associated with saddlenode bifurcations is imperative in a broad range of sciences and for a wide variety of purposes, including ecological assessment, signal amplification, and microscale mass sensing. In many such practices, noise and non-stationarity are unavoidable and everpresent influences. As a result, it is critical to simul...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2006
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.1859