Modeling of Multilinear Dynamical Systems from Experimental Data

2009 ◽  
pp. 183-197
Author(s):  
Jasek Kluska
Keyword(s):  
Experimental Data ◽  
Dynamical Systems

scholarly journals A computational framework for finding parameter sets associated with chaotic dynamics

2021 ◽  
pp. 1-11
Author(s):  
S. Koshy-Chenthittayil ◽  
E. Dimitrova ◽  
E.W. Jenkins ◽  
B.C. Dean
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Parameter Space ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Computational Framework ◽  
Independent Variables ◽  
Systems Model ◽  
Small Support

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.

THREE TYPES OF SIMPLE DDE'S DESCRIBING TUMOR GROWTH

2007 ◽  
Vol 15 (04) ◽  
pp. 453-471 ◽  
Author(s):  
MAREK BODNAR ◽  
URSZULA FORYŚ
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Tumor Growth ◽  
Delay Differential Equations ◽  
Ehrlich Ascites Tumor ◽  
Ascites Tumor ◽  
Ehrlich Ascites ◽  
Delay Differential

In this paper, we compare three types of dynamical systems used to describe tumor growth. These systems are defined as solutions to three delay differential equations: the logistic, the Gompertz and the Greenspan types. We present analysis of these systems and compare with experimental data for Ehrlich Ascites tumor in mice.

Modeling the dynamical systems on experimental data

1996 ◽  
Author(s):  
Natalie B. Janson ◽  
Vadim S. Anishchenko
Keyword(s):  
Experimental Data ◽  
Dynamical Systems

scholarly journals On the Concept of Complexity of Random Dynamical Systems

1998 ◽  
Vol 12 (03) ◽  
pp. 225-243 ◽  
Author(s):  
V. Loreto ◽  
M. Serva ◽  
A. Vulpiani
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Random Perturbation ◽  
Point Of View ◽  
Random Dynamical Systems ◽  
Random Perturbations ◽  
Physical Point ◽  
Random Maps ◽  
Numerical Examples ◽  
Real Experimental Data

We show how to introduce a characterization the "complexity" of random dynamical systems. More precisely we propose a suitable indicator of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by these systems. This indicator of complexity, which can be extracted from real experimental data, turns out to be very natural in the context of information theory. For dynamical systems with random perturbations, it coincides with the rate K of divergence of nearby trajectories evolving under two different noise realizations. In presence of strong dynamical intermittency, the value of K is very different from the standard Lyapunov exponent λσ computed through the consideration of two nearby trajectories evolving under the same realization of the random perturbation. However, the former is much more relevant than the latter from a physical point of view as illustrated by some numerical examples of noisy and random maps.

scholarly journals A dynamical systems approach for estimating phase interactions between rhythms of different frequencies from experimental data

2018 ◽  
Vol 14 (1) ◽  
pp. e1005928 ◽  
Author(s):  
Takayuki Onojima ◽  
Takahiro Goto ◽  
Hiroaki Mizuhara ◽  
Toshio Aoyagi
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Systems Approach

scholarly journals Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Edward G. Belaga ◽  
Maurice Mignotte
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Discrete Dynamical Systems ◽  
Experimental Results ◽  
Diophantine Representation ◽  
Random Behavior ◽  
International Audience ◽  
Collatz Problem

International audience Building on theoretical insights and rich experimental data of our preprints, we present here new theoretical and experimental results in three interrelated approaches to the Collatz problem and its generalizations: \emphalgorithmic decidability, random behavior, and Diophantine representation of related discrete dynamical systems, and their \emphcyclic and divergent properties.

Sign in / Sign up

Export Citation Format

Share Document