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

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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

How Fertilizers Contribute to Lower Food Costs.

8 p

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 $[0,1]$ 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