title: Sequential memory: Binding dynamics.
abstract: Temporal order memories are critical for everyday animal and human functioning. Experiments and our own experience show that the binding or association of various features of an event together and the maintaining of multimodality events in sequential order are the key components of any sequential memories-episodic, semantic, working, etc. We study a robustness of binding sequential dynamics based on our previously introduced model in the form of generalized Lotka-Volterra equations. In the phase space of the model, there exists a multi-dimensional binding heteroclinic network consisting of saddle equilibrium points and heteroclinic trajectories joining them. We prove here the robustness of the binding sequential dynamics, i.e., the feasibility phenomenon for coupled heteroclinic networks: for each collection of successive heteroclinic trajectories inside the unified networks, there is an open set of initial points such that the trajectory going through each of them follows the prescribed collection staying in a small neighborhood of it. We show also that the symbolic complexity function of the system restricted to this neighborhood is a polynomial of degree L - 1, where L is the number of modalities.
authors.affiliation: IICO-UASLP, Karakorum 1470, Lomas 4a, San Luis Potosi, SLP 78210, Mexico.
authors.forename: Valentin
authors.initials: V
authors.lastname: Afraimovich
authors.affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701, USA.
authors.forename: Xue
authors.initials: X
authors.lastname: Gong
authors.affiliation: BioCircuits Institute, University of California San Diego, 9500 Gilman Dr., La Jolla, California 92093-0328, USA.
authors.forename: Mikhail
authors.initials: M
authors.lastname: Rabinovich
mesh_terms: D006801:Humans; D008570:Memory, Short-Term / Q000502:physiology*; D008959:Models, Neurological