## MAP-PDMA

**Wolfram Erlhagen**

*CMAT - University of Minho*

**Abstract ::**

Dynamic Neural Fields (DNFs) formalized by nonlinear integro-differential equations have been originally introduced as a model framework for explaining basic principles of neural information processing in which the interactions of billions of neurons are treated as a continuum. The intention is to reduce the enormous complexity of neural interactions to simpler population properties that are tractable by mathematical analysis. More recently, complex models consisting of several connected DNFs have been developed to explain higher level cognitive functions (e.g., memory, decision making, prediction and learning) and to implement these functionalities in autonomous robots. I will give an overview about the physiological motivation of DNFs, the mathematical analysis of their dynamic behaviors, and their application in cognitive robotics. As an example study, I focus on “multi-bump” solutions that have been proposed as a neural substrate for a multi-item memory function. I show how the existence and stability properties of these solutions can be exploited to endow a robot with the capacity to efficiently learn the timing and serial order of sequential events. I also discuss new mathematical challenges that are motivated by robotics applications.

**References**

[1] S.-I. Amari (1977). Dynamics of pattern formation in lateral-inhibition type neural fields, Biological Cybernetics 27 (2), 77-87.

[2] W. Erlhagen, E. Bicho (2006). The dynamic neural eld approach to cognitive robotics, Journal of Neural Engineering 3 (3), R36.

[3] F. Ferreira., W. Erlhagen, E. Bicho (2016). Multi-bump solutions in a neural eld model with external inputs. Physica D: Nonlinear Phenomena, 326, 32-51.

[4] W. Wojtak, S. Coombes, D. Avitabile, E. Bicho, W. Erlhagen (2021). A dynamic neural eld model of continuous input integration. Biological Cybernetics, 1-21.

[5] F. Ferreira, W. Wojtak, E. Sousa, L. Louro, E. Bicho, W. Erlhagen (2020). Rapid learning of complex sequences with time constraints: A dynamic neural eld model. IEEE Transactions on Cognitive and Developmental Systems. DOI: 10.1109/TCDS.2020.2991789

Seminar for the Doctoral Program in Applied Mathematics (MAP-PDMA Seminar)