Abstract: Based on the orthogonality of Banach spaces and analogous to the method of simplifying operator equations using Liapunov Schmidt, a Liapunov Schmidt scheme is derived for converting bifurcation equations into finite dimensional or low dimensional algebraic equations. Determine the bifurcation point of the simplified bifurcation equation, and calculate the partial derivative value at the bifurcation point to construct a smooth function strongly equivalent to the bifurcation equation .When the constructed smooth function satisfies the same condition as the partial derivative of the Pitchfork bifurcation equation at the bifurcation point, the smooth function is strongly equivalent to the Pitchfork bifurcation equation. The condition satisfied by the partial derivative is the necessary and sufficient condition for identifying Pitchfork bifurcations, enriching the identification methods of bifurcations in Banach spaces.
张诗畦, 许静波. Banach空间中Pitchfork分岔的识别[J]. 吉林化工学院学报, 2025, 42(5): 95-98.
Xu Jingbo, Zhang Shiqi . Recognition of Pitchfork Bifurcation in Banach Spaces. Journal of Jilin Institute of Chemical Technology, 2025, 42(5): 95-98.
