3,753 research outputs found
Global convergence of quorum-sensing networks
In many natural synchronization phenomena, communication between individual
elements occurs not directly, but rather through the environment. One of these
instances is bacterial quorum sensing, where bacteria release signaling
molecules in the environment which in turn are sensed and used for population
coordination. Extending this motivation to a general non- linear dynamical
system context, this paper analyzes synchronization phenomena in networks where
communication and coupling between nodes are mediated by shared dynamical quan-
tities, typically provided by the nodes' environment. Our model includes the
case when the dynamics of the shared variables themselves cannot be neglected
or indeed play a central part. Applications to examples from systems biology
illustrate the approach.Comment: Version 2: minor editions, added section on noise. Number of pages:
36
Dual symplectic classical circuits: An exactly solvable model of many-body chaos
We propose a general exact method of calculating dynamical correlation
functions in dual symplectic brick-wall circuits in one dimension. These are
deterministic classical many-body dynamical systems which can be interpreted in
terms of symplectic dynamics in two orthogonal (time and space) directions. In
close analogy with quantum dual-unitary circuits, we prove that two-point
dynamical correlation functions are non-vanishing only along the edges of the
light cones. The dynamical correlations are exactly computable in terms of a
one-site Markov transfer operator, which is generally of infinite
dimensionality. We test our theory in a specific family of dual-symplectic
circuits, describing the dynamics of a classical Floquet spin chain.
Remarkably, for these models, the rotational symmetry leads to a transfer
operator with a block diagonal form on the basis of spherical harmonics. This
allows us to obtain analytical predictions for simple local observables. We
demonstrate the validity of our theory by comparison with Montecarlo
simulations, displaying excellent agreement for different choices of
observables.Comment: 16 pages, 5 figure
- …