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- W2012808738 abstract "Let $A(u,alpha)=F_u(u,alpha)$ ($u in R^n, alpha in R^k$) be a family of real $n times n$ matrices arising as the Jacobian matrices of equilibrium solutions to the dynamical system $ stackrel{.}{u}=F(u,alpha)$. An equilibrium point is called a Hopf point if A has a conjugate pair of pure imaginary eigenvalues $pm iomega$, $omega> 0$. It is called a double Hopf point if there are two such pairs $pm iomega_1, pm iomega_2$ and a 1:1 resonant double Hopf point if, in addition, $omega_1=omega_2$. Defining functions are obtained for the numerical detection, computation, and continuation of Hopf, double Hopf, and 1:1 resonant double Hopf points. They are based on a combination of matrix biproduct and bordered matrix methods. Example computations are done in a fairly realistic and complicated neural model problem with $n=13$ and $k=29$. However, to make the methods applicable to large-scale problems (e.g., discretized boundary value problems) we reduce the state space to a subspace that essentially contains the generalized eigenspaces of the eigenvalues with largest real part." @default.
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- W2012808738 date "1997-06-01" @default.
- W2012808738 modified "2023-09-25" @default.
- W2012808738 title "Defining Functions for Multiple Hopf Bifurcations" @default.
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- W2012808738 doi "https://doi.org/10.1137/s0036142995282182" @default.
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