Quick search Find article
Quick search
Find article

Control of dynamic Hopf bifurcations

N Berglund

Show affiliations


Recommended by A I Neishtadt

The slow passage through a Hopf bifurcation leads to the delayed appearance of large-amplitude oscillations. We construct a smooth scalar feedback control which suppresses the delay and causes the system to follow a stable equilibrium branch. This feature can be used to detect in time the loss of stability of an ageing device. As a by-product, we obtain results on the slow passage through a bifurcation with double-zero eigenvalue, described by a singularly perturbed cubic Liénard equation.


PACS

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

02.30.Yy Control theory

02.30.Hq Ordinary differential equations

02.30.Oz Bifurcation theory

MSC

93B52 Feedback control

34C23 Bifurcation (See mainly 37Gxx)

34H05 Control problems (See also 49J25, 49K25, 93C15)

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 1 (January 2000)

Received 1 April 1999, in final form 23 September 1999



  1. Control of dynamic Hopf bifurcations

    N Berglund 2000 Nonlinearity 13 225

  2. K and L X-ray excitation in very-heavy-ion-atom collisions near K-L level matching

    A Warczak et al 1983 J. Phys. B: At. Mol. Phys. 16 1575

  3. Merger of the UK National Radiological Protection Board with the Health Protection Agency

    John Cooper and Parvaiz Ali 2005 J. Radiol. Prot. 25 221

  4. Canonical strangeness and distillation effects in hadron production

    V D Toneev and A S Parvan 2005 J. Phys. G: Nucl. Part. Phys. 31 583

  5. Size-dependent optical properties and carriers dynamics in CdSe/ZnS quantum dots

    Ma Hong et al 2008 Chinese Phys. B 17 1280

  6. Diffusion by anti-structure defects in non-stoichiometric intermetallic compounds with B2 and structures

    S V Divinski and L N Larikov 1997 J. Phys.: Condens. Matter 9 7873

  7. Half-metallic ferromagnets. II. Transport properties of NiMnSb and related inter-metallic compounds

    M J Otto et al 1989 J. Phys.: Condens. Matter 1 2351

  8. The importance of spin-orbit coupling in the magnetised hydrogen problem

    G Wunner et al 1985 J. Phys. B: At. Mol. Phys. 18 L179

  9. Symbolic dynamics of almost collision orbits and skew products of symplectic maps

    Sergey Bolotin 2006 Nonlinearity 19 2041

  10. Units for quantities of dimension one

    René Dybkaer 2004 Metrologia 41 69

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.