P075 Sequential dynamical invariants in winnnerless competition neural networks
Irene Elices*1, Pablo Varona1 1 Grupo de Neurocomputación Biológica, Dept. de Ingeniería Informática, Escuela Politécnica Superior, Universidad Autónoma de Madrid, 28049, Madrid, Spain.
*Email: irene.elices@uam.es Introduction
Generating neural sequences is fundamental for behavior and cognition, which require robustness of sequential order and flexibility in its time intervals to adapt effectively. Studying cyclic sequences provides key insights into constraints limiting flexibility and shaping sequence intervals. Previously, we identified such constraints as robust cycle-by-cycle relationships between specific time intervals, i.e., dynamical invariants, in bursting central pattern generators [1]. However, their presence in computational models remains largely unexplored. Here, we examine dynamical invariants in a winnerless competition network model that generates chaotic activity while sustaining robust sequences among active neurons.
Methods We analyzed sequence interval relationships in a Lotka-Volterra neural network that displays chaotic heteroclinic dynamics from its asymmetric connectivity [2,3]. Variables in these generalized Lotka-Volterra differential equations represent the instantaneous spike rate of the neurons. For analysis, we selected the most active neuron as a cycle reference, detecting sequential events in other neurons using activation thresholds. Cycle-by-cycle intervals were defined as the time intervals between activation and subsequent deactivation events, including those between distinct neurons. Analysis included variability measures, correlation analysis, and PCA to uncover robust relationships between interval timings.
Results Despite the chaotic dynamics, which can be related to exploration tasks in motor and cognitive activity [2-4], we observed robust dynamical invariants between specific time intervals that added to the activation phase locks in active neurons to provide coordination between cells. The dynamical invariants represent constraints to the variability present in the chaotic activity and can underlie an emergent control mechanism. This is the first time that sequential dynamical invariants are reported in heteroclinic dynamics.
Discussion The presence of dynamical invariants remains largely unexplored in computational models, with only a few studies addressing simplified circuits, such as minimal CPG circuit building blocks [5]. The main challenge in studying dynamical invariants in computational models is the lack of variability in individual model neurons and in network dynamics. However, a winnerless competition network model generates chaotic spatiotemporal activation patterns, thus overcoming the mentioned variability challenge. Our work analyzes for the first time the presence of dynamical invariants among the activation intervals. Results suggest that these robust cycle-by-cycle relationships are part of the sequence coordination mechanisms of the heteroclinic dynamics.
Acknowledgements Work funded by PID2021-122347NB-I00, PID2024-155923NB-I00, and CPP2023-010818 (MCIN/AEI and ERDF- “A way of making Europe”). References [1]https://doi.org/10.1038/s41598-019-44953-2 [2]https://doi.org/10.1063/1.1498155 [3]https://doi.org/10.1103/PhysRevE.71.061909 [4]https://doi.org/10.1007/s11571-023-09987-3
