Local Bifurcations and a Survey of Bounded Quadratic Systems

This paper presents online methods for controlling local bifurcations of power grids with the goal of increasing bifurcation values (i.e. increasing load margins) via network topology optimization, a low-cost control. In other words, this paper presents online methods for increasing power transfer capability subject to static stability limit via switching transmission line out/in (i.e. disconnecting a transmission line or connecting a transmission line). To illustrate the impact of network topology on local bifurcations, two common local bifurcations, i.e. saddle-node bifurcation and structure-induced bifurcation on small power grids with different network topologies are shown. A three-stage online control methodology of local bifurcations via network topology optimization is presented to delay local bifurcations of power grids. Online methods must meet the challenging requirements of online applications such as the speed requirement (in the order of minutes), accuracy requirement and robustness requirement. The effectiveness of the three-stage methodology for online applications is demonstrated on the IEEE 118-bus and a 1648-bus practical power systems.

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Local Bifurcations in the Symmetric Model of Selection with Fertility Differences

Journal of Theoretical Biology ◽

10.1006/jtbi.1997.0514 ◽

1997 ◽

Vol 189 (3) ◽

pp. 291-295 ◽

Cited By ~ 2

Author(s):

Krešimir Josić

Keyword(s):

Symmetric Model ◽

Local Bifurcations

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Stability analysis and guaranteed cost control for stochastic nonlinear quadratic systems

2015 European Control Conference (ECC) ◽

10.1109/ecc.2015.7330704 ◽

2015 ◽

Author(s):

Alessio Merola ◽

Francesco Amato

Keyword(s):

Stability Analysis ◽

Cost Control ◽

Guaranteed Cost Control ◽

Quadratic Systems ◽

Guaranteed Cost

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Resonances and Torsion Numbers of Driven Dissipative Nonlinear Oscillators

Zeitschrift für Naturforschung A ◽

10.1515/zna-1986-0404 ◽

1986 ◽

Vol 41 (4) ◽

pp. 605-614 ◽

Cited By ~ 14

Author(s):

Ulrich Parlitz ◽

Werner Lauterborn

Keyword(s):

Nonlinear Oscillators ◽

Winding Number ◽

Local Flow ◽

One Dimensional ◽

Bifurcation Set ◽

Local Bifurcations ◽

Closed Orbits

The torsion of the local flow around closed orbits and its relation to the superstructure in the bifurcation set of strictly dissipative nonlinear oscillators is investigated. The torsion number describing the twisting behaviour of the flow turns out to be a suitable invariant for the classification of local bifurcations and resonances in those systems. Furthermore, the notions of winding number and resonance are generalized to arbitrary one-dimensional dissipative oscillators.

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Bifurcation Analysis and Optimal Harvesting of a Delayed Predator–Prey Model

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127415500121 ◽

2015 ◽

Vol 25 (01) ◽

pp. 1550012 ◽

Cited By ~ 1

Author(s):

P. Tchinda Mouofo ◽

R. Djidjou Demasse ◽

J. J. Tewa ◽

M. A. Aziz-Alaoui

Keyword(s):

Natural Resource Management ◽

Optimal Control Theory ◽

Uniform Boundedness ◽

Optimal Harvesting ◽

Global Dynamics ◽

Saddle Node Bifurcation ◽

Predator Prey ◽

Predator Prey Model ◽

Local Bifurcations ◽

Prey Model

A delay predator–prey model is formulated with continuous threshold prey harvesting and Holling response function of type III. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. The positive invariance of the non-negative orthant is proved and the uniform boundedness of the trajectories. Stability of equilibria is investigated and the existence of some local bifurcations is established: saddle-node bifurcation, Hopf bifurcation. We use optimal control theory to provide the correct approach to natural resource management. Results are also obtained for optimal harvesting. Numerical simulations are given to illustrate the results.

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