The Mathematical Biology Seminar series presents Xue Gong on “Robustness of binding heteroclinic networks—a model in sequential memory” on Tuesday, Nov. 10, from 5:10 pm to 6:10 p.m. in Morton 131. (Note new location.)
Xue Gong
Abstract: Most of human cognitive activities like talking face-to-face, singing, making decisions are based on the dynamics of sequential working memory (SWM). Information items of SWM in such activities can be classified into several informational modalities. We can think of the information items in each informational modality as a metastable state and the mind sequentially switches from one metastable state to another in a certain order to bind the information together. For example, a singer binds the lyrics, melody, and rhythm together to produce the song.
In this talk, the speaker will present the joint work with Drs. Valentin Afraimovich and Mikhail Rabinovich. We study the mathematical aspect of a model in SWM. This model is a high-dimensional ODE system in the form of generalized Lotka-Volterra equations. The mathematical image of this model in the phase space is a heteroclinic chain of heteroclinic cycles, which we call a binding heteroclinic network. We prove the robustness of the binding heteroclinic networks, i.e., for each collection of successive heteroclinic trajectories inside the uni ed networks, there is an open set of initial points such that the trajectory going through each of them follows the prescribed collection of heteroclinic trajectories and stays in a small neighborhood of it. We also show that the symbolic complexity function of the system restricted to this neighborhood is a polynomial. Therefore, the system is not chaotic.
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