755 research outputs found
Signal buffering in random networks of spiking neurons: microscopic vs. macroscopic phenomena
In randomly connected networks of pulse-coupled elements a time-dependent
input signal can be buffered over a short time. We studied the signal buffering
properties in simulated networks as a function of the networks state,
characterized by both the Lyapunov exponent of the microscopic dynamics and the
macroscopic activity derived from mean-field theory. If all network elements
receive the same signal, signal buffering over delays comparable to the
intrinsic time constant of the network elements can be explained by macroscopic
properties and works best at the phase transition to chaos. However, if only 20
percent of the network units receive a common time-dependent signal, signal
buffering properties improve and can no longer be attributed to the macroscopic
dynamics.Comment: 5 pages, 3 figure
Additional information on
Of pendulums, polymers, and robots: Computational mechanics with constraints Am. J. Phys. 81, 537 (2013) Solving for three-dimensional central potentials using numerical matrix methods Am. J. Phys. 81, 343 (2013) Computational problems in introductory physics: Lessons from a bead on a wire Am. J. Phys. 81, 165 (2013) Solution of the quantum initial value problem with transparent boundary conditions Am. J. Phys. 81, 50 (2013) Additional information on Am. J. Phys. Many phenomena in the real world are inherently complex and involve many dynamical variables interacting nonlinearly through feedback loops and exhibiting chaos, self-organization, and pattern formation. It is useful to ask if there are generic features of such systems, and if so, how simple can such systems be and still display these features. This paper describes several such systems that are accessible to undergraduates and might serve as useful examples of complexity
Geometric and dynamic perspectives on phase-coherent and noncoherent chaos
Statistically distinguishing between phase-coherent and noncoherent chaotic
dynamics from time series is a contemporary problem in nonlinear sciences. In
this work, we propose different measures based on recurrence properties of
recorded trajectories, which characterize the underlying systems from both
geometric and dynamic viewpoints. The potentials of the individual measures for
discriminating phase-coherent and noncoherent chaotic oscillations are
discussed. A detailed numerical analysis is performed for the chaotic R\"ossler
system, which displays both types of chaos as one control parameter is varied,
and the Mackey-Glass system as an example of a time-delay system with
noncoherent chaos. Our results demonstrate that especially geometric measures
from recurrence network analysis are well suited for tracing transitions
between spiral- and screw-type chaos, a common route from phase-coherent to
noncoherent chaos also found in other nonlinear oscillators. A detailed
explanation of the observed behavior in terms of attractor geometry is given.Comment: 12 pages, 13 figure
Time's Barbed Arrow: Irreversibility, Crypticity, and Stored Information
We show why the amount of information communicated between the past and
future--the excess entropy--is not in general the amount of information stored
in the present--the statistical complexity. This is a puzzle, and a
long-standing one, since the latter is what is required for optimal prediction,
but the former describes observed behavior. We layout a classification scheme
for dynamical systems and stochastic processes that determines when these two
quantities are the same or different. We do this by developing closed-form
expressions for the excess entropy in terms of optimal causal predictors and
retrodictors--the epsilon-machines of computational mechanics. A process's
causal irreversibility and crypticity are key determining properties.Comment: 4 pages, 2 figure
Simple models of complex chaotic systems
Many phenomena in the real world are inherently complex and involve many dynamical variables interacting nonlinearly through feedback loops and exhibiting chaos, self-organization, and pattern formation. It is useful to ask if there are generic features of such systems, and if so, how simple can such systems be and still display these features. This paper describes several such systems that are accessible to undergraduates and might serve as useful examples of complexity
Visualizing the logistic map with a microcontroller
The logistic map is one of the simplest nonlinear dynamical systems that
clearly exhibit the route to chaos. In this paper, we explored the evolution of
the logistic map using an open-source microcontroller connected to an array of
light emitting diodes (LEDs). We divided the one-dimensional interval
into ten equal parts, and associated and LED to each segment. Every time an
iteration took place a corresponding LED turned on indicating the value
returned by the logistic map. By changing some initial conditions of the
system, we observed the transition from order to chaos exhibited by the map.Comment: LaTeX, 6 pages, 3 figures, 1 listin
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