CELLULAR-AUTOMATON-CONTROLLED LOGISTIC MAP: AN UNUSUAL TYPE OF NOISE

1992 ◽  
Vol 03 (03) ◽  
pp. 547-552
Author(s):  
DANIEL A. STARIOLO ◽  
CONSTANTINO TSALLIS
Keyword(s):  
Cellular Automaton ◽  
Internal Structure ◽  
Numerical Study ◽  
Logistic Map ◽  
Time Dependent ◽  
Dependent Parameter ◽  
Multiple Band ◽  
Parameter Values ◽  
Unusual Type

We present a numerical study of the logistic map dynamics with time dependent parameter values whose evolution is in turn governed by a deterministic cellular automaton. We find an unusual type of noise which presents a surprising internal structure yielding a multiple band attractor.

scholarly journals The timing of contact restrictions and pro-active testing balances the socio-economic impact of a lockdown with the control of infections

2020 ◽  
Author(s):  
Saptarshi Bej ◽  
Olaf Wolkenhauer
Keyword(s):  
Mathematical Models ◽  
Time Dependent ◽  
Simulation Studies ◽  
Epidemiological Models ◽  
Extensive Documentation ◽  
Active Testing ◽  
Dependent Parameter ◽  
Socio Economic Impact ◽  
Parameter Values

During the SARS-CoV-2 pandemic, numerous mathematical models have been developed. Reporting artefacts and missing data about asymptomatic spreaders, imply considerable margins of uncertainty for model-based predictions. Epidemiological models can however also be used to investigate the consequences of measures to control the pandemic, reflected in changes to parameter values. We present a SIR-based, SUIR model in which the influence of testing and a reduction of contacts is studied by distinguishing 'Unidentified' and 'Identified' spreaders of infections. The model uses four ordinary differential equations and is kept deliberately simple to investigate general patterns occurring from testing and contact restrictions. The model goes beyond other efforts, by introducing time dependent parameter curves that represent different strategies in controlling the pandemic. Our analysis reveals the effect of 'pro-active' testing for the design of contact restriction measures. By pro-active testing we mean testing beyond those people who show symptoms. The simulations can explain why the timing of contract restrictions and pro-active testing is important. The model can also be used to study the consequence of different strategies to exit from lockdown. Our SUIR model is implemented in Python and is made available through a Juypter Notebooks. This an extensive documentation of the derivation and implementation of the model, as well as transparent and reproducible simulation studies. Our model should contribute to a better understanding of the role of testing and contact restrictions.

A NUMERICAL STUDY OF UNIVERSALITY AND SELF-SIMILARITY IN SOME FAMILIES OF FORCED LOGISTIC MAPS

2013 ◽  
Vol 23 (04) ◽  
pp. 1350072 ◽  
Author(s):  
PAU RABASSA ◽  
ÀNGEL JORBA ◽  
JOAN CARLES TATJER
Keyword(s):  
Bifurcation Diagram ◽  
Numerical Study ◽  
Logistic Map ◽  
Finite Sequence ◽  
Invariant Curves ◽  
Self Similarity ◽  
Consecutive Period ◽  
Parametric Families ◽  
The One ◽  
Parameter Values

We explore different two-parametric families of quasi-periodically Forced Logistic Maps looking for universality and self-similarity properties. In the bifurcation diagram of the one-dimensional Logistic Map, it is well known that there exist parameter values sn where the 2n-periodic orbit is superattracting. Moreover, these parameter values lay between the parameters corresponding to two consecutive period doublings. In the quasi-periodically Forced Logistic Maps, these points are replaced by invariant curves, that undergo a (finite) sequence of period doublings. In this work, we study numerically the presence of self-similarities in the bifurcation diagram of the invariant curves of these quasi-periodically Forced Logistic Maps. Our computations show a remarkable self-similarity for some of these families. We also show that this self-similarity cannot be extended to any quasi-periodic perturbation of the Logistic map.

The solution of an infinite set of differential-difference equations occurring in polymerization and queueing problems

1963 ◽  
Vol 59 (1) ◽  
pp. 117-124 ◽  
Author(s):  
A. Wragg
Keyword(s):  
Difference Equations ◽  
Queueing Theory ◽  
Bessel Functions ◽  
Formal Solution ◽  
Monomer Concentration ◽  
Arrival Rate ◽  
Time Dependent ◽  
Type Integral ◽  
Dependent Parameter ◽  
Infinite Set

AbstractThe time-dependent solutions of an infinite set of differential-difference equations arising from queueing theory and models of ‘living’ polymer are expressed in terms of modified Bessel functions. Explicit solutions are available for constant values of a parameter describing the arrival rate or monomer concentration; for time-dependent parameter a formal solution is obtained in terms of a function which satisfies a Volterra type integral equation of the second kind. These results are used as the basis of a numerical method of solving the infinite set of differential equations when the time-dependent parameter itself satisfies a differential equation.

scholarly journals Time-Dependent Material Properties of Shotcrete: Experimental and Numerical Study

Materials ◽  
2017 ◽  
Vol 10 (9) ◽  
pp. 1067 ◽  
Author(s):  
Matthias Neuner ◽  
Tobias Cordes ◽  
Martin Drexel ◽  
Günter Hofstetter
Keyword(s):  
Material Properties ◽  
Numerical Study ◽  
Time Dependent

scholarly journals Evolution of a domain wall in expanding universe: inflation and after it

2018 ◽  
Vol 191 ◽  
pp. 08004
Author(s):  
A.D. Dolgov ◽  
S.I. Godunov ◽  
A.S. Rudenko
Keyword(s):  
Domain Wall ◽  
Hubble Parameter ◽  
Domain Walls ◽  
Flat Space ◽  
Space Time ◽  
Time Dependent ◽  
Expanding Universe ◽  
Large Size ◽  
Dependent Parameter ◽  
Thick Domain Walls

We study the evolution of thick domain walls in the expanding universe. We have found that the domain wall evolution crucially depends on the time-dependent parameter C(t) = 1/(H(t)δ0)2, where H(t) is the Hubble parameter and δ0 is the width of the wall in flat space-time. For C(t) > 2 the physical width of the wall, a(t)δ(t), tends with time to constant value δ0, which is microscopically small. Otherwise, when C(t) ≤ 2, the wall steadily expands and can grow up to a cosmologically large size.

A case study in bifurcation theory

2017 ◽  
Vol 28 (08) ◽  
pp. 1750104 ◽  
Author(s):  
Youssef Khmou
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Theory ◽  
Chaotic Behavior ◽  
Numerical Study ◽  
Logistic Map ◽  
Logistic Function ◽  
Second Order ◽  
Short Paper ◽  
Chaotic Region

This short paper is focused on the bifurcation theory found in map functions called evolution functions that are used in dynamical systems. The most well-known example of discrete iterative function is the logistic map that puts into evidence bifurcation and chaotic behavior of the topology of the logistic function. We propose a new iterative function based on Lorentizan function and its generalized versions, based on numerical study, it is found that the bifurcation of the Lorentzian function is of second-order where it is characterized by the absence of chaotic region.

STABILIZATION OF CHAOTIC DYNAMICS OF ONE-DIMENSIONAL MAPS BY A CYCLIC PARAMETRIC TRANSFORMATION

1996 ◽  
Vol 06 (04) ◽  
pp. 725-735 ◽  
Author(s):  
ALEXANDER Yu. LOSKUTOV ◽  
VALERY M. TERESHKO ◽  
KONSTANTIN A. VASILIEV
Keyword(s):  
Periodic Orbits ◽  
Chaotic Dynamics ◽  
Chaotic Maps ◽  
Logistic Map ◽  
Exponential Map ◽  
One Dimensional ◽  
Stable Periodic ◽  
One Dimensional Maps ◽  
Parameter Values ◽  
Parametric Transformation

We consider one-dimensional maps, the logistic map and an exponential map, in those sets of parameter values which correspond to their chaotic dynamics. It is proven that such dynamics may be stabilized by a certain cyclic parametric transformation operating strictly within the chaotic set. The stabilization is a result of the creation of stable periodic orbits in the initially chaotic maps. The period of these stable orbits is a multiple of the period of the cyclic transformation. It is shown that stabilized behavior cannot be destroyed by a weak noise smearing of the required parameter values. The regions where the behavior stabilization takes place are numerically estimated. Periods of the created stabile periodic orbits are calculated.

A numerical study of synchronization in the process of biochemical substance exchange in a diffusively coupled ring of cells

Open Physics ◽  
2013 ◽  
Vol 11 (4) ◽  
Author(s):  
Dragutin Mihailović ◽  
Igor Balaž ◽  
Ilija Arsenić
Keyword(s):  
Kolmogorov Complexity ◽  
Numerical Study ◽  
Logistic Map ◽  
Sample Entropy ◽  
Cell System ◽  
Negotiation Process ◽  
Cell Affinity ◽  
Basic Features ◽  
Biochemical Substance ◽  
Different Levels

AbstractIn this paper we numerically investigate a model of a diffusively coupled ring of cells. To model the dynamics of individual cells we propose a map with cell affinity, which is a generalization of the logistic map. First, the basic features of a one-cell system are studied in terms of the Lyapunov exponent, Kolmogorov complexity and Sample Entropy. Second, the notion of observational heterarchy, which is a perpetual negotiation process between different levels of the description of a phenomenon, is reviewed. After these preliminaries, we study how the active coupling induced by the consideration of the observational heterarchy modifies the synchronization property of the model with N=100 cells. It is shown numerically that the active coupling enhances synchronization of biochemical substance exchange in several different conditions of cell affinity.

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