Information capacity and pattern formation in a tent map network featuring statistical periodicity

Abstract

We provide quantitative support to the observation that lattices of coupled maps are "efficient" information coding devices. It has been suggested recently that lattices of coupled maps may provide a model of information coding in the nervous system because of their ability to create structured and stimulus-dependent activity patterns which have the potential to be used for storing information. In this paper, we give an upper bound to the effective number of patterns that can be used to store information in the lattice by evaluating numerically its information capacity or information rate as a function of the coupling strength between the maps. We also estimate the time taken by the lattice to establish a limiting activity pattern.

Complexity measures from interaction structures

“…Tent map lattices are a well established model to study synchronization and pattern formation in spatially extended systems [15,16]. We will study binary symbolic dynamics of coupled tent map network [17,18].…”

Locking-time and Information Capacity in CML with Statistical Periodicity

“…where ε ∈ [0, 1] is the coupling strength between the sites of the lattice and f (x) is local dynamics. Following [7] we consider…”

“…CMLs with statistical periodicity were studied in [6,7] driven by experimentally observed features in neural network. Hauptmann et al [7] show that the CML can reproduce such features when the coupling is weak.…”

“…CMLs with statistical periodicity were studied in [6,7] driven by experimentally observed features in neural network. Hauptmann et al [7] show that the CML can reproduce such features when the coupling is weak. However, they determined the time for the lattice to achieve the permanent periodic state or locking-time using a somewhat primitive method.…”

Inducing Periodicity in Lattices of Chaotic Maps with Advection

“…Such networks of maps were applied e.g. to model information coding [7], to study nonlinear wave-like patterns [8], ocean convection parameterization [9], synchronization processes [10,11].…”