Effects of Small Time Delays on Continuous System Performance

1994 ◽  
pp. 615-617
Keyword(s):  
System Performance ◽  
Time Delays ◽  
Continuous System ◽  
Small Time

scholarly journals Evolution of populations with strategy-dependent time delays

2019 ◽  
Author(s):  
Jacek Miȩkisz ◽  
Marek Bodnar
Keyword(s):  
Stationary State ◽  
Time Delays ◽  
Replicator Dynamics ◽  
Evolutionarily Stable Strategy ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Small Time ◽  
Stochastic Perturbations ◽  
New Type ◽  
Novel Behavior

AbstractWe address the issue of stability of coexistence of two strategies with respect to time delays in evolving populations. It is well known that time delays may cause oscillations. Here we report a novel behavior. We show that a microscopic model of evolutionary games with a unique mixed evolutionarily stable strategy (a globally asymptotically stable interior stationary state in the standard replicator dynamics) and with strategy-dependent time delays leads to a new type of replicator dynamics. It describes the time evolution of fractions of the population playing given strategies and the size of the population. Unlike in all previous models, an interior stationary state of such dynamics depends continuously on time delays and at some point it might disappear, no cycles are present. In particular, this means that an arbitrarily small time delay changes an interior stationary state. Moreover, at certain time delays, there may appear another interior stationary state.Author summarySocial and biological processes are usually described by ordinary or partial differential equations, or by Markov processes if we take into account stochastic perturbations. However, interactions between individuals, players or molecules, naturally take time. Results of biological interactions between individuals may appear in the future, and in social models, individuals or players may act, that is choose appropriate strategies, on the basis of the information concerning events in the past. It is natural therefore to introduce time delays into evolutionary game models. It was usually observed, and expected, that small time delays do not change the behavior of the system and large time delays may cause oscillations. Here we report a novel behavior. We show that microscopic models of evolutionary games with strategy-dependent time delays, in which payoffs appear some time after interactions of individuals, lead to a new type of replicator dynamics. Unlike in all previous models, interior stationary states of such dynamics depend continuously on time delays. This shows that effects of time delays are much more complex than it was previously thought.

scholarly journals Approximate stationary densities, and parameter estimations for time-delayed stochastic logistic growth laws

2007 ◽  
Vol 47 ◽  
Author(s):  
Petras Rupšys
Keyword(s):  
Growth Model ◽  
Time Delays ◽  
Single Species ◽  
Small Time ◽  
Logistic Growth ◽  
Estimation Of Parameters ◽  
Stationary Distributions ◽  
Parameter Estimations ◽  
Growth Laws ◽  
Delayed Growth

We consider stochastic logistic type delayed growth model (Verhulst, Gompertz, Richards) of a single species population.The objective of this paper is to deduce a procedureon the estimation of parameters. We derive approximate stationary distributions in the case of small time delays. For the estimate of parameters we apply the L1 distance procedure. We propose approximate estimations of the parameters.

scholarly journals Synchronization by small time delays

2015 ◽  
Vol 420 ◽  
pp. 8-13 ◽  
Author(s):  
G. Pruessner ◽  
S. Cheang ◽  
H.J. Jensen
Keyword(s):  
Time Delays ◽  
Small Time

Performance of time-delay estimators

Geophysics ◽  
2005 ◽  
Vol 70 (4) ◽  
pp. V109-V120 ◽  
Author(s):  
Claudio Bagaini
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Signal To Noise Ratio ◽  
Linear Equations ◽  
Reference Signal ◽  
Synthetic Data ◽  
Original Data ◽  
Small Time ◽  
Time Delay Estimation ◽  
Estimation Accuracy

I analyze the problem of estimating differences in the arrival times of a seismic wavefront recorded by an array of sensors. The two-sensor problem is tackled first, showing that even an approximate knowledge of the wavelet, such as its power spectrum, can substantially increase the accuracy of the time-delay estimate and reduce the signal-to-noise ratio (S/N) threshold for reliable time-delay estimation. The use of the complex trace, although beneficial for time-delay estimates in the presence of frequency-independent phase shifts, reduces the estimation accuracy in poor S/N conditions. I compare the performance of five time-delay estimators for arrays of sensors. Four of five estimators are based on crosscorrelation with a reference signal derived according to one of the following criteria: one trace in the array randomly selected, the stack of all array traces, the stack of all array traces iteratively updated, and (possible only for synthetic data) the noise-free wavelet. Another method, which is referred to as integration of differential delays, is based on the solution of an overdetermined system of linear equations built using the time delays between each pair of sensors. In all the situations considered, the performance of crosscorrelation with a trace of the array randomly selected is significantly worse than the other methods. Integration of differential delays proved to be the best-performing method for a large range of S/N conditions, particularly in the presence of large fluctuations in time delays and large bandwidth. However, for small time delays with respect to the wavelet duration, or if a priori knowledge of the moveout can be used to detrend the original data, crosscorrelation with a stacked trace performs similarly to integration of differential delays.

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