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.

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.

A Numerical Study of New Logistic Map

2018 ◽  
Vol 17 (02) ◽  
pp. 1871001
Author(s):  
Youssef Khmou
Keyword(s):  
Traffic Flow ◽  
Bifurcation Diagram ◽  
Random Number ◽  
Numerical Study ◽  
Random Sequence ◽  
Logistic Map ◽  
Growth Parameter ◽  
Random Number Generation ◽  
Macroscopic Model ◽  
Optimal Velocity

In this paper, we propose a new logistic map based on the relation of the information entropy, we study the bifurcation diagram comparatively to the standard logistic map. In the first part, we compare the obtained diagram, by numerical simulations, with that of the standard logistic map. It is found that the structures of both diagrams are similar where the range of the growth parameter is restricted to the interval [0,e]. In the second part, we present an application of the proposed map in traffic flow using macroscopic model. It is found that the bifurcation diagram is an exact model of the Greenberg’s model of traffic flow where the growth parameter corresponds to the optimal velocity and the random sequence corresponds to the density. In the last part, we present a second possible application of the proposed map which consists of random number generation. The results of the analysis show that the excluded initial values of the sequences are (0,1).

scholarly journals Analytical solution of one-dimensional Pennes’ bioheat equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1084-1092
Author(s):  
Hongyun Wang ◽  
Wesley A. Burgei ◽  
Hong Zhou
Keyword(s):  
Analytical Solution ◽  
Radiofrequency Energy ◽  
Bioheat Equation ◽  
Surface Cooling ◽  
One Dimensional ◽  
The Fourier Transform ◽  
The One ◽  
Parameter Values ◽  
Mathematical Derivation ◽  
Effect Of Surface

Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

scholarly journals Thermal-stress analysis of a damaged solid sphere using hyperbolic two-temperature generalized thermoelasticity theory

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hamdy M. Youssef ◽  
Alaa A. El-Bary ◽  
Eman A. N. Al-Lehaibi
Keyword(s):  
Mechanical Damage ◽  
Generalized Thermoelasticity ◽  
Solid Sphere ◽  
Thermoelasticity Theory ◽  
Mechanical Waves ◽  
Temperature Parameter ◽  
Thermoelastic Solid ◽  
The One ◽  
Parameter Values ◽  
Two Temperature

AbstractThis work aims to study the influence of the rotation on a thermoelastic solid sphere in the context of the hyperbolic two-temperature generalized thermoelasticity theory based on the mechanical damage consideration. Therefore, a mathematical model of thermoelastic, homogenous, and isotropic solid sphere with a rotation based on the mechanical damage definition has been constructed. The governing equations have been written in the context of hyperbolic two-temperature generalized thermoelasticity theory. The bounding surface of the sphere is thermally shocked and without volumetric deformation. The singularities of the studied functions at the center of the sphere have been deleted using L’Hopital’s rule. The numerical results have been represented graphically with various mechanical damage values, two-temperature parameters, and rotation parameter values. The two-temperature parameter has significant effects on all the studied functions. Damage and rotation have a major impact on deformation, displacement, stress, and stress–strain energy, while their effects on conductive and dynamical temperature rise are minimal. The thermal and mechanical waves propagate with finite speeds on the thermoelastic body in the hyperbolic two-temperature theory and the one-temperature theory (Lord-Shulman model).

On the numerical study of thermohydrodynamics and biochemistry of inland water bodies

2021 ◽  
Author(s):  
Daria Gladskikh ◽  
Evgeny Mortikov ◽  
Victor Stepanenko
Keyword(s):  
Mixed Layer ◽  
Numerical Study ◽  
Three Dimensional ◽  
Water Bodies ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Lake Model ◽  
Upper Mixed Layer ◽  
The One

<p>The study of thermodynamic and biochemical processes of inland water objects using one- and three-dimensional RANS numerical models was carried out both for idealized water bodies and using measurements data. The need to take into account seiche oscillations to correctly reproduce the deepening of the upper mixed layer in one-dimensional (vertical) models is demonstrated. We considered the one-dimensional LAKE model [1] and the three-dimensional model [2, 3, 4] developed at the Research Computing Center of Moscow State University on the basis of a hydrodynamic code combining DNS/LES/RANS approaches for calculating geophysical turbulent flows. The three-dimensional model was supplemented by the equations for calculating biochemical substances by analogy with the one-dimensional biochemistry equations used in the LAKE model. The effect of mixing processes on the distribution of concentration of greenhouse gases, in particular, methane and oxygen, was studied.</p><p>The work was supported by grants of the RF President’s Grant for Young Scientists (MK-1867.2020.5, MD-1850.2020.5) and by the RFBR (19-05-00249, 20-05-00776). </p><p>1. Stepanenko V., Mammarella I., Ojala A., Miettinen H., Lykosov V., Timo V. LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes // Geoscientific Model Development. 2016. V. 9(5). P. 1977–2006.<br>2. Mortikov E.V., Glazunov A.V., Lykosov V.N. Numerical study of plane Couette flow: turbulence statistics and the structure of pressure-strain correlations // Russian Journal of Numerical Analysis and Mathematical Modelling. 2019. 34(2). P. 119-132.<br>3. Mortikov, E.V. Numerical simulation of the motion of an ice keel in stratified flow // Izv. Atmos. Ocean. Phys. 2016. V. 52. P. 108-115.<br>4. Gladskikh D.S., Stepanenko V.M., Mortikov E.V. On the influence of the horizontal dimensions of inland waters on the thickness of the upper mixed layer // Water Resourses. 2021.V. 45, 9 pages. (in press) </p>

scholarly journals Optimal Portfolios for Financial Markets with Wishart Volatility

2013 ◽  
Vol 50 (4) ◽  
pp. 1025-1043 ◽  
Author(s):  
Nicole Bäuerle ◽  
Zejing Li
Keyword(s):  
Value Function ◽  
Numerical Study ◽  
Heston Model ◽  
Hard Part ◽  
Control Approach ◽  
Portfolio Strategy ◽  
Hamilton Jacobi Bellman ◽  
The One ◽  
Hedging Demand ◽  
The Value Function

We consider a multi asset financial market with stochastic volatility modeled by a Wishart process. This is an extension of the one-dimensional Heston model. Within this framework we study the problem of maximizing the expected utility of terminal wealth for power and logarithmic utility. We apply the usual stochastic control approach and obtain, explicitly, the optimal portfolio strategy and the value function in some parameter settings. In particular, we do this when the drift of the assets is a linear function of the volatility matrix. In this case the affine structure of the model can be exploited. In some cases we obtain a Feynman-Kac representation of the candidate value function. Though the approach we use is quite standard, the hard part is to identify when the solution of the Hamilton-Jacobi-Bellman equation is finite. This involves a couple of matrix analytic arguments. In a numerical study we discuss the influence of the investors' risk aversion on the hedging demand.

GLOBAL BEHAVIOR OF THE CHARGED ISOSCELES THREE-BODY PROBLEM

1994 ◽  
Vol 04 (04) ◽  
pp. 865-884 ◽  
Author(s):  
PAU ATELA ◽  
ROBERT I. McLACHLAN
Keyword(s):  
Bifurcation Diagram ◽  
Periodic Orbits ◽  
Body Problem ◽  
Kepler Problem ◽  
Global Bifurcation ◽  
Three Body Problem ◽  
Anisotropic Kepler Problem ◽  
The One ◽  
Three Body ◽  
Limiting Value

We study the global bifurcation diagram of the two-parameter family of ODE’s that govern the charged isosceles three-body problem. (The classic isosceles three-body problem and the anisotropic Kepler problem (two bodies) are included in the same family.) There are two major sources of periodic orbits. On the one hand the “Kepler” orbit, a stable orbit exhibiting the generic bifurcations as the multiplier crosses rational values. This orbit turns out to be the continuation of the classical circular Kepler orbit. On the other extreme we have the collision-ejection orbit which exhibits an “infinite-furcation.” Up to a limiting value of the parameter we have finitely many periodic orbits (for each fixed numerator in the rotation number), passed this value there is a sudden birth of an infinite number of them. We find that these two bifurcations are remarkably connected forming the main “skeleton” of the global bifurcation diagram. We conjecture that this type of global connection must be present in related problems such as the classic isosceles three-body problem and the anisotropic Kepler problem.

scholarly journals Signaling pathways have an inherent need for noise to acquire information

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Eugenio Azpeitia ◽  
Eugenio P. Balanzario ◽  
Andreas Wagner
Keyword(s):  
Signaling Pathways ◽  
Information Acquisition ◽  
Cellular Level ◽  
Kinetic Properties ◽  
Positive Role ◽  
Binding Interactions ◽  
Reversible Binding ◽  
Wide Range ◽  
The One ◽  
Parameter Values

Abstract Background All living systems acquire information about their environment. At the cellular level, they do so through signaling pathways. Such pathways rely on reversible binding interactions between molecules that detect and transmit the presence of an extracellular cue or signal to the cell’s interior. These interactions are inherently stochastic and thus noisy. On the one hand, noise can cause a signaling pathway to produce the same response for different stimuli, which reduces the amount of information a pathway acquires. On the other hand, in processes such as stochastic resonance, noise can improve the detection of weak stimuli and thus the acquisition of information. It is not clear whether the kinetic parameters that determine a pathway’s operation cause noise to reduce or increase the acquisition of information. Results We analyze how the kinetic properties of the reversible binding interactions used by signaling pathways affect the relationship between noise, the response to a signal, and information acquisition. Our results show that, under a wide range of biologically sensible parameter values, a noisy dynamic of reversible binding interactions is necessary to produce distinct responses to different stimuli. As a consequence, noise is indispensable for the acquisition of information in signaling pathways. Conclusions Our observations go beyond previous work by showing that noise plays a positive role in signaling pathways, demonstrating that noise is essential when such pathways acquire information.

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.

Sign in / Sign up

Export Citation Format

Share Document