Name
Abstract | ||
|---|---|---|
This paper addresses the problems of characterizing and estimating the bifurcation sets of equilibrium points in multi-parameter space of a class of nonlinear dynamical systems. Specifically, we investigate the sets of parameters that lead to saddle-node bifurcations and Hopf bifurcations at an equilibrium point of interest. First, a characterization of these sets is provided in terms of the zeros of some functions. Second, this characterization is exploited to estimate such sets through convex programming for the case of polynomial dynamical systems. In particular, two conditions are proposed for establishing whether a sublevel set of a given polynomial does not contain parameters that lead to bifurcations. By using these conditions, the largest of such sublevel sets can be estimated by solving an eigenvalue problem. Some numerical examples illustrate the proposed results. |
Year | Venue | Keywords |
|---|---|---|
2013 | Control Conference | bifurcation,convex programming,eigenvalues and eigenfunctions,nonlinear dynamical systems,hopf bifurcations,bifurcation sets,eigenvalue problem,equilibrium points,multi parameter space,polynomial dynamical systems,saddle-node bifurcations,vectors,estimation,polynomials |
Field | DocType | Citations |
Discrete mathematics,Applied mathematics,Linear dynamical system,Projected dynamical system,Bifurcation diagram,Bifurcation theory,Dynamical systems theory,Transcritical bifurcation,Hopf bifurcation,Mathematics,Saddle-node bifurcation | Conference | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Graziano Chesi | 1 | 1386 | 116.41 |
| Gouhei Tanaka | 2 | 51 | 11.80 |
| Hirata, Y. | 3 | 0 | 0.34 |
| Kazuyuki Aihara | 4 | 1909 | 333.03 |