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Complete Mean-Field Theory for Dynamics of Binary Recurrent Networks
Farzad Farkhooi1,2, Wilhelm Stannat1,2
1Institut für Mathematik, Technische Universität Berlin, 10623 Berlin,Germany.
Abstract:
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.
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