# Remembering to learn

Understanding the dynamics of networks of memristors, a new paradigm for low-power computation inspired by the structure of the brain.

Memristors are resistors that preserve memory. They can be used to regulate and limit the amount of current that flows through a circuit, as they are able to change the value of their resistance based on their memory of the current and the voltage in the network.

This project investigates how an analytical description of simple memristive circuits can be used to understand the properties of more complicated networks of memristors. Our overall approach uses idealised models where the dynamics can be solved exactly to uncover emergent behaviour. For example, we explore the relationship between the topology of the circuit and the dynamics of memristors using techniques from graph theory. Using mean field theory, we identify the asymptotic behaviour of memristor dynamics beyond the linear regime. We verify our analytic results with numerical solutions, demonstrating the ability of simple models to explain the collective behaviour of complex networks.

The idea that memristors have internal memory means that it is possible for a network of them to learn. This ability can be harnessed to implement models of neural systems, and hence study and mimic the brain. It also makes memristors a potential alternative paradigm for solid-state memory.

#### Related papers

#### Exactly solvable model of memristive circuits: Lyapunov functional and mean field theory

F. Caravelli, P. Barucca

*European Physical Journal B*

#### The mise en scene of memristive networks: effective memory, dynamics and learning

F. Caravelli

*International Journal of Parallel, Emergent and Distributed Systems*

#### The complex dynamics of memristive circuits: analytical results and universal slow relaxation

F. Caravelli, F. Traversa, M. Ventra

*Physical Review E*