↓ Skip to main content

Complex dynamics of memristive circuits: Analytical results and universal slow relaxation

Overview of attention for article published in Physical Review E, February 2017
Altmetric Badge

Mentioned by

1 tweeter
1 Wikipedia page


5 Dimensions

Readers on

14 Mendeley
Complex dynamics of memristive circuits: Analytical results and universal slow relaxation
Published in
Physical Review E, February 2017
DOI 10.1103/physreve.95.022140
Pubmed ID

F. Caravelli, F. L. Traversa, M. Di Ventra


Networks with memristive elements (resistors with memory) are being explored for a variety of applications ranging from unconventional computing to models of the brain. However, analytical results that highlight the role of the graph connectivity on the memory dynamics are still few, thus limiting our understanding of these important dynamical systems. In this paper, we derive an exact matrix equation of motion that takes into account all the network constraints of a purely memristive circuit, and we employ it to derive analytical results regarding its relaxation properties. We are able to describe the memory evolution in terms of orthogonal projection operators onto the subspace of fundamental loop space of the underlying circuit. This orthogonal projection explicitly reveals the coupling between the spatial and temporal sectors of the memristive circuits and compactly describes the circuit topology. For the case of disordered graphs, we are able to explain the emergence of a power-law relaxation as a superposition of exponential relaxation times with a broad range of scales using random matrices. This power law is also universal, namely independent of the topology of the underlying graph but dependent only on the density of loops. In the case of circuits subject to alternating voltage instead, we are able to obtain an approximate solution of the dynamics, which is tested against a specific network topology. These results suggest a much richer dynamics of memristive networks than previously considered.

Twitter Demographics

The data shown below were collected from the profile of 1 tweeter who shared this research output. Click here to find out more about how the information was compiled.

Mendeley readers

The data shown below were compiled from readership statistics for 14 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 14 100%

Demographic breakdown

Readers by professional status Count As %
Professor 3 21%
Student > Doctoral Student 2 14%
Researcher 2 14%
Student > Postgraduate 2 14%
Student > Master 2 14%
Other 3 21%
Readers by discipline Count As %
Physics and Astronomy 4 29%
Computer Science 3 21%
Unspecified 2 14%
Chemistry 2 14%
Engineering 2 14%
Other 1 7%