A Dynamical Systems Model of Grammatical Innovation

2011 ◽  
Author(s):  
Whitney Tabor
2021 ◽  
pp. 1-11
Author(s):  
S. Koshy-Chenthittayil ◽  
E. Dimitrova ◽  
E.W. Jenkins ◽  
B.C. Dean

Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we use existing software tools (COPASI, R) to explore dynamical systems and uncover regions with positive Lyapunov exponents where thus chaos exists. We evaluate the ability of the software’s optimization algorithms to find these positive values with several dynamical systems used to model biological populations. The algorithms have been able to identify parameter sets which lead to positive Lyapunov exponents, even when those exponents lie in regions with small support. For one of the examined systems, we observed that positive Lyapunov exponents were not uncovered when executing a search over the parameter space with small spacings between values of the independent variables.


2005 ◽  
Vol 72 (4) ◽  
Author(s):  
Srevatsan Muralidharan ◽  
K. R. Sreenivas ◽  
Rama Govindarajan

2014 ◽  
Vol 15 (S1) ◽  
Author(s):  
Houman Safaai ◽  
Ricardo Neves ◽  
Oxana Eschenko ◽  
Nikos K Logothetis ◽  
Stefano Panzeri

1999 ◽  
Vol 394 ◽  
pp. 205-240 ◽  
Author(s):  
S. V. GORDEYEV ◽  
F. O. THOMAS

Fourier and wavelet transformation techniques are utilized in a complementary manner in order to characterize temporal aspects of the transition of a planar jet shear layer. The subharmonic is found to exhibit an interesting temporal amplitude and phase variation that has not been previously reported. This takes the form of intermittent π-shifts in subharmonic phase between two fixed phase values. These phase jumps are highly correlated with local minima of the subharmonic amplitude. In contrast, the fundamental amplitude and phase show no such behaviour. The temporal phase behaviour of the subharmonic has the effect of intermittently disrupting the phase lock with the fundamental. A dynamical systems model is developed which is based on a classic vortex representation of the shear layer. The Hamiltonian formulation of the problem is shown to provide remarkable agreement with the experimental results. All the essential aspects of the temporal amplitude and phase behaviour of the subharmonic are reproduced by the model including amplitude-dependent effects. The model is also shown to provide a dynamical systems based explanation for time-averaged amplitude and phase behaviour observed in these as well as earlier experiments. The results of experiments involving both bimodal forcing at fundamental and subharmonic frequencies with prescribed initial effective phase angle as well as experiments involving only fundamental excitation over an amplitude range extending two orders of magnitude are presented. The temporal subharmonic amplitude and phase behaviour is observed in bimodal forcing experiments in those regions of the flow characterized by subharmonic mode suppression and vortex tearing events (even if the forcing amplitudes are quite large). In addition, temporal subharmonic amplitude and phase behaviour is the rule in experiments involving low-amplitude forcing of the fundamental and the natural development of the subharmonic.


2019 ◽  
Vol 16 (159) ◽  
pp. 20190311 ◽  
Author(s):  
Daniel Galvis ◽  
Darren Walsh ◽  
Lorna W. Harries ◽  
Eva Latorre ◽  
James Rankin

Senescent cells provide a good in vitro model to study ageing. However, cultures of ‘senescent’ cells consist of a mix of cell subtypes (proliferative, senescent, growth-arrested and apoptotic). Determining the proportion of senescent cells is crucial for studying ageing and developing new anti-degenerative therapies. Commonly used markers such as doubling population, senescence-associated β-galactosidase, Ki-67, γH2AX and TUNEL assays capture diverse and overlapping cellular populations and are not purely specific to senescence. A newly developed dynamical systems model follows the transition of an initial culture to senescence tracking population doubling, and the proportion of cells in proliferating, growth-arrested, apoptotic and senescent states. Our model provides a parsimonious description of transitions between these states accruing towards a predominantly senescent population. Using a genetic algorithm, these model parameters are well constrained by an in vitro human primary fibroblast dataset recording five markers at 16 time points. The computational model accurately fits to the data and translates these joint markers into the first complete description of the proportion of cells in different states over the lifetime. The high temporal resolution of the dataset demonstrates the efficacy of strategies for reconstructing the trajectory towards replicative senescence with a minimal number of experimental recordings.


Author(s):  
Cesar A. Martin ◽  
Daniel E. Rivera ◽  
William T. Riley ◽  
Eric B. Hekler ◽  
Matthew P. Buman ◽  
...  

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