Mixed-mode oscillations and dynamics analysis in a pituitary cell model
Feibiao Zhan
Shenquan Liu
Bo Lu 
Xiaohan Zhang
Jing Wang

so Bursting is an intrinsic pattern of electrical activ-ity in excitable cells such as endocrine cells and many types of neurons. The technique of slow-fast dynamics analysis is helpful in analyzing two subsystem with time scales vary widely. In this paper, we acquired a deeper understanding of the dynamics of a novel form of bursting (pseudo-plateau)from the system with three differential equations extend to the bifurcation analysis for the full system. We mainly ex-plored the existence of mixed-mode oscillations (MMOs)and dynamical behaviors in the pituitary cell via using slow-fast analysis and bifurcation theory, respectively. First, we investigated the mixed-mode oscillations by numerical cal-culation and theoretical method, and showed bursting elec-trical pattern by the graphic rendering. In addition, the first Lyapunov coefficient of the Hopf bifurcation was comput-ed to determine whether it is subcritical or supercritical to further explain the behaviors of bursting. Moreover, we also took the codimension-two bifurcation analysis for the e-quilibrium of the full system and observed a great many b-ifurcation points with abundant behaviors. Finally, we ob-tained the concrete expression of the pituitary cell model for a saddle-node bifurcation curve, a Hopf bifurcation curve and a saddle homoclinic curve via theoretical derivation n-ear the Bogdanov-Takens bifurcation point.

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