We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description of nonequilibrium fluctuations in networks with a finite size and finite degree of interactions. Our approach allows the investigation of systems for which a deterministic mean-field theory breaks down. To demonstrate this, we uncover a novel dynamic state in which a recurrent network of binary units with statistically inhomogeneous interactions, along with an asynchronous behavior, also exhibits collective nontrivial stochastic fluctuations in the thermodynamical limit.
Physical Review Letters
- Pub Date:
- November 2017
- Physics - Biological Physics;
- Condensed Matter - Disordered Systems and Neural Networks;
- Quantitative Biology - Neurons and Cognition;
- 5 pages, 2 figures, Accepted (Physical Review Letters)