Imperfect Bifurcation in Structures and Materials by Kiyohiro Ikeda & Kazuo Murota

Author:Kiyohiro Ikeda & Kazuo Murota
Language: eng
Format: epub
ISBN: 9783030214739
Publisher: Springer International Publishing

For θ = α k the Hessian matrix is diagonal, since . For the diagonal entries, we use (9.60) and (9.61), as well as by θ = α k, to obtain

Therefore, the Hessian matrix is positive-definite (in the asymptotic sense) if and only if

(9.68)

and

(9.69)

Therefore, the half-branch for θ = α k is stable if (9.68) and (9.69) hold. Then we obtain the following.

For , all half-branches are unstable.

For , the stability of the bifurcating paths is dependent on the signs of A 0300 and A 2100 ± A 0300.

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