Terminal Transient Phase of Chaotic Transients

An analysis was made to determine the relation between spike timing and the intensity of a constant current evoking a repetitive discharge in the single lobster motor axon. Accurate measurements of repetition intervals during the transient phase showed that an intensity increase of about 10–3 rheobase units produces a significantly different change in spike interval timing at the 0.005 probability level. Applications of excitation theory to the latency-intensity data have produced an equation which predicts the latency to the nth spike in a repetitive sequence as a function of stimulus intensity. The equation implies that the excitation process producing the nth spike is similar to the process producing the first spike in the repetitive sequence. Influences of supernormality and refractoriness were incorporated into the analysis. Also repeated stimulation at a fixed intensity indicated an inherent variability in the timing of the repetitive response which was shown to be a function of the magnitude of the latency. To explain this result a fixed uncertainty in the level of the initiating excitatory state was postulated.

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Scaling behavior of the terminal transient phase

Physical Review E ◽

10.1103/physreve.98.022215 ◽

2018 ◽

Vol 98 (2) ◽

Cited By ~ 3

Author(s):

Thomas Lilienkamp ◽

Ulrich Parlitz

Keyword(s):

Scaling Behavior ◽

Transient Phase

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Structure and dynamical behavior of non-normal networks

Science Advances ◽

10.1126/sciadv.aau9403 ◽

2018 ◽

Vol 4 (12) ◽

pp. eaau9403 ◽

Cited By ~ 23

Author(s):

Malbor Asllani ◽

Renaud Lambiotte ◽

Timoteo Carletti

Keyword(s):

Network Science ◽

Wide Spectrum ◽

Dynamical Behavior ◽

Transient Phase ◽

The Stability ◽

Normal Networks ◽

Empirical Networks ◽

Peculiar Behavior ◽

Potential Use ◽

Small Disturbances

We analyze a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behavior, as initial small disturbances may undergo a transient phase and be strongly amplified in linearly stable systems. In addition, eigenvalues may become extremely sensible to noise and have a diminished physical meaning. We identify structural properties of networks that are associated with non-normality and propose simple models to generate networks with a tunable level of non-normality. We also show the potential use of a variety of metrics capturing different aspects of non-normality and propose their potential use in the context of the stability of complex ecosystems.

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