Looking at map networks with time delay interactions
from a local perspective
Autores: A. Parravano
Referencia: Physica A, 371, 767, (2006)
Abstract
The evolution of networks of coupled chaotic maps with delayed
interactions can be studied in the usual way by analyzing the
evolution of the state of elements at each iteration time (the
``Simulator'' point of view), or it can be analyzed from the
point of view of a single element (the ``Observer''
perspective) that is receiving delayed information from the
other elements in the system. In the usual ``Simulator''
timeframe, an absolute time (i.e. the number of iterations
$t$) is adopted to define the system state at each time $t$.
In the ``Observer'' framework, the state of an element in
the system is given by its state at the ``Simulator'' time
$t-\tau$, where $\tau$ is the information travel time
between that element and the Observer. We emphasize the
convenience of the analysis of the system dynamics in the
``Observer'' timeframe by showing that the ``Observer''
dynamics differs substantially from the one in the
``Simulator'' timeframe, and that the system dynamics
in the ``Observer'' timeframe reflects the proper
causality of the interactions among the elements.
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