منابع مشابه
Hopf Bifurcation and Stability in DAEs
A simple comparison of the areas of the sciences in which DAEs are involved with those in which examples of Hopf bifurcation in ODEs arise (see Thompson and Stewart (1986) and the references therein) reveals a considerable overlap and suggests that an appropriate variant of the Hopf bifurcation theorem should be available in the DAE setting. In this chapter, we show that, indeed, a generalizati...
متن کاملStability and Hopf Bifurcation in the Watt Governor System
The Watt centrifugal governor is a device that automatically controls the speed of an engine. Dating to 1788, it can be taken as the starting point for automatic control theory (see MacFarlane [5] and references therein). In this paper the system coupling the Watt-centrifugal-governor and the steamengine will be called simply the Watt Governor System (WGS). Landmarks for the study of the local ...
متن کاملStability and Hopf Bifurcation Analysis of the Delay Logistic Equation
Logistic functions are good models of biological population growth. They are also popular in marketing in modelling demand-supply curves and in a different context, to chart the sales of new products over time. Delays being inherent in any biological system, we seek to analyse the effect of delays on the growth of populations governed by the logistic equation. In this paper, the local stability...
متن کاملStability analysis of a noise-induced Hopf bifurcation
We study analytically and numerically the noise-induced transition between an absorbing and an oscillatory state in a Duffing oscillator subject to multiplicative, Gaussian white noise. We show in a non-perturbative manner that a stochastic bifurcation occurs when the Lyapunov exponent of the linearised system becomes positive. We deduce from a simple formula for the Lyapunov exponent the phase...
متن کاملHOPF BIFURCATION CONTROL WITH PD CONTROLLER
In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1979
ISSN: 0022-247X
DOI: 10.1016/0022-247x(79)90207-5