Observational constraints of emergent universe in brane-world with Gauss–Bonnet term and dissipative effect

2019 ◽  
Vol 16 (11) ◽  
pp. 1950169 ◽  
Author(s):  
Partha Sarathi Debnath
Keyword(s):  
Equilibrium Points ◽  
Brane World ◽  
Model Parameters ◽  
Type Ii ◽  
Emergent Universe ◽  
World Model ◽  
Imperfect Fluid ◽  
The Stability ◽  
Bonnet Term ◽  
The Eu

Cosmological solutions in the Randall–Sundrum (RS) type II brane-world model including Gauss–Bonnet (GB) term, in the presence of a bulk viscous cosmological fluid are discussed. Transport equations described by Eckart and Israel Stewart are implemented here. Cosmological models admitting emergent universe (EU) of the early universe is explored here in the presence of imperfect fluid described by Eckart theory and Truncated Israel Stewart (TIS) theory and Full Israel Stewart (FIS) theory. We also study the permitted values of the EU model parameters by considering cosmological observational dataset. The stability analysis of the equilibrium points of the dynamical system associated with the evolution in the RS brane including GB term are studied in Eckart theory, TIS theory and FIS theory.

scholarly journals WARPED BRANE-WORLD COMPACTIFICATION WITH GAUSS–BONNET TERM

2003 ◽  
Vol 18 (15) ◽  
pp. 2703-2727 ◽  
Author(s):  
Y. M. CHO ◽  
I. P. NEUPANE
Keyword(s):  
Effective Action ◽  
Planck Scale ◽  
Delta Function ◽  
Einstein Gravity ◽  
Brane World ◽  
Warp Factor ◽  
Second Derivative ◽  
World Model ◽  
Bonnet Term ◽  
Kaluza Klein

In the Randall–Sundrum (RS) brane-world model a singular delta-function source is matched by the second derivative of the warp factor. So one should take possible curvature corrections in the effective action of the RS models in the Gauss–Bonnet (GB) form. We present a linearized treatment of gravity in the RS brane-world with the Gauss–Bonnet modifications to Einstein gravity. We give explicit expressions for the Neumann propagator in arbitrary D dimensions and show that a bulk GB term gives, along with a tower of Kaluza–Klein modes in the bulk, a massless graviton on the brane, as in the standard RS model. Moreover, a nontrivial GB coupling can allow a new branch of solutions with finite Planck scale and no naked bulk singularity, which might be useful to avoid some of the previously known "no-go theorems" for RS brane-world compactifications.

scholarly journals On approximate solutions for a fractional prey–predator model involving the Atangana–Baleanu derivative

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Behzad Ghanbari
Keyword(s):  
Fractional Derivative ◽  
Numerical Technique ◽  
Equilibrium Points ◽  
Approximate Solutions ◽  
Model Parameters ◽  
Uniqueness Of Solutions ◽  
Fractional Systems ◽  
The Third ◽  
Predator Model ◽  
The Stability

AbstractMathematical modeling has always been one of the most potent tools in predicting the behavior of dynamic systems in biology. In this regard, we aim to study a three-species prey–predator model in the context of fractional operator. The model includes two competing species with logistic growing. It is considered that one of the competitors is being predated by the third group with Holling type II functional response. Moreover, one another competitor is in a commensal relationship with the third category acting as its host. In this model, the Atangana–Baleanu fractional derivative is used to describe the rate of evolution of functions in the model. Using a creative numerical trick, an iterative method for determining the numerical solution of fractional systems has been developed. This method provides an implicit form for determining solution approximations that can be solved by standard methods in solving nonlinear systems such as Newton’s method. Using this numerical technique, approximate answers for this system are provided, assuming several categories of possible choices for the model parameters. In the continuation of the simulations, the sensitivity analysis of the solutions to some parameters is examined. Some other theoretical features related to the model, such as expressing the necessary conditions on the stability of equilibrium points as well as the existence and uniqueness of solutions, are also examined in this article. It is found that utilizing the concept of fractional derivative order the flexibility of the model in justifying different situations for the system has increased. The use of fractional operators in the study of other models in computational biology is recommended.

scholarly journals Is the addition of higher-order interactions in ecological models increasing the understanding of ecological dynamics?

2019 ◽  
Author(s):  
Mohammad AlAdwani ◽  
Serguei Saavedra
Keyword(s):  
Equilibrium Points ◽  
Explanatory Power ◽  
Higher Order ◽  
Ecological Models ◽  
Model Parameters ◽  
Ecological Communities ◽  
Ecological Dynamics ◽  
Higher Order Terms ◽  
Population Dynamics Models ◽  
The Stability

AbstractRecent work has shown that higher-order interactions can increase the stability, promote the diversity, and better explain the dynamics of ecological communities. Yet, it remains unclear whether the perceived benefits of adding higher-order terms into population dynamics models come from fundamental principles or a simple mathematical advantage given by the nature of multivariate polynomials. Here, we develop a general method to quantify the mathematical advantage of adding higher-order interactions in ecological models based on the number of free-equilibrium points that can be engineered in a system (i.e., equilibria that can be feasible or unfeasible by tunning model parameters). We apply this method to calculate the number of free-equilibrium points in Lotka-Volterra dynamics. While it is known that Lotka-Volterra models without higher-order interactions only have one free-equilibrium point regardless of the number of parameters, we find that by adding higher-order terms this number increases exponentially with the dimension of the system. Our results suggest that while adding higher-order interactions in ecological models may be good for prediction purposes, they cannot provide additional explanatory power of ecological dynamics if model parameters are not ecologically restricted.

scholarly journals Observational constrains on the DGP brane-world model with a Gauss–Bonnet term in the bulk

2007 ◽  
Vol 654 (5-6) ◽  
pp. 133-138 ◽  
Author(s):  
Jian-Hua He ◽  
Bin Wang ◽  
Eleftherios Papantonopoulos
Keyword(s):  
Brane World ◽  
World Model ◽  
Bonnet Term

Observational constraints of emergent universe in f(R,T) gravity with bulk viscosity

2020 ◽  
Vol 17 (07) ◽  
pp. 2050102
Author(s):  
Partha Sarathi Debnath ◽  
Bikash Chandra Paul
Keyword(s):  
Bulk Viscosity ◽  
Modified Gravity ◽  
Equilibrium Points ◽  
Momentum Tensor ◽  
General Function ◽  
Emergent Universe ◽  
Data Set ◽  
Cosmological Solutions ◽  
Coupling Parameters ◽  
The Eu

Emergent universe (EU) cosmological models with viscosity in a modified gravity which contains a general function [Formula: see text], where [Formula: see text] and [Formula: see text] denote the curvature scalar and the trace of the energy–momentum tensor, respectively, are studied in a flat Friedmann–Robertson–Walker metric. Cosmological solutions are obtained in [Formula: see text] theory of gravity, which represented as [Formula: see text] with bulk viscosity that described by Eckart theory, truncated Israel Stewart theory and full Israel Stewart Theory. The physical and geometrical features of the EU models in [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] are coupling parameters, with bulk viscosity are studied in details. Constraints of the EU models parameters in [Formula: see text] gravity with bulk viscosity are estimated from observational data set. The stability analysis of the equilibrium points admitting cosmological solutions of the dynamical system associated with the evolution in the modified gravity is studied in Eckart theory, truncated Israel Stewart theory and full Israel Stewart theory.

Emergent universe model with dissipative effects

2017 ◽  
Vol 32 (39) ◽  
pp. 1750216 ◽  
Author(s):  
P. S. Debnath ◽  
B. C. Paul
Keyword(s):  
General Theory ◽  
Universe Model ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Emergent Universe ◽  
Dissipative Effects ◽  
Cosmological Observations ◽  
Cosmological Solutions ◽  
The Stability ◽  
The Eu

Emergent universe model is presented in general theory of relativity with isotropic fluid in addition to viscosity. We obtain cosmological solutions that permit emergent universe scenario in the presence of bulk viscosity that are described by either Eckart theory or Truncated Israel Stewart (TIS) theory. The stability of the solutions are also studied. In this case, the emergent universe (EU) model is analyzed with observational data. In the presence of viscosity, one obtains emergent universe scenario, which however is not permitted in the absence of viscosity. The EU model is compatible with cosmological observations.

scholarly journals A Mathematical Model for the Eradication of Anopheles Mosquito and Elimination of Malaria

2020 ◽  
pp. 1-14
Author(s):  
Atanyi Yusuf Emmanuel ◽  
Abam Ayeni Omini
Keyword(s):  
Mathematical Model ◽  
Life Cycle ◽  
Steady State ◽  
Stability Analysis ◽  
Equilibrium State ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
Anopheles Mosquito ◽  
Model Parameters ◽  
The Stability

A mathematical model to eliminate malaria by breaking the life cycle of anopheles mosquito using copepods at larva stage and tadpoles at pupa stage was derived aimed at eradicating anopheles pupa mosquito by introduction of natural enemies “copepods and tadpoles” (an organism that eats up mosquito at larva and pupa stage respectively). The model equations were derived using the model parameters and variables. The stability analysis of the free equilibrium states was analyzed using equilibrium points of Beltrami and Diekmann’s conditions for stability analysis of steady state. We observed that the model free equilibrium state is stable which implies that the equilibrium point or steady state is stable and the stability of the model means, there will not be anopheles adult mosquito in our society for malaria transmission. The ideas of Beltrami’s and Diekmann conditions revealed that the determinant and trace of the Jacobian matrix were greater than zero and less than zero respectively implying that the model disease free equilibrium state is stable. Hence, the number of larva that transforms to pupa is almost zero while the pupa that develop to adult is zero meaning the life-cycle is broken at the larva and pupa stages with the introduction of natural enemy. Maple was used for the symbolic and numerical solutions.

scholarly journals Stability analysis of DGP brane-world model with agegraphic dark energy

2020 ◽  
Vol 98 (8) ◽  
pp. 778-783
Author(s):  
A. Ravanpak ◽  
G.F. Fadakar
Keyword(s):  
Dark Energy ◽  
Stability Analysis ◽  
System Approach ◽  
Phase Plane ◽  
Jacobi Matrix ◽  
Brane World ◽  
Coincidence Problem ◽  
World Model ◽  
Agegraphic Dark Energy ◽  
The Stability

The aim of this work is to apply the dynamical system approach to study the linear dynamics of the normal DGP brane-world model with agegraphic dark energy. The stability analysis of the model will be investigated and the phase plane portrait will be illustrated. The nature of critical points will be analyzed by evaluating the eigenvalues of a linearized Jacobi matrix. Also, the statefinder diagnostic procedure will be applied to show the slight deviation of our model from the ΛCDM model. One of the most interesting results of this work is the great alleviation of the coincidence problem.

Political aspects of security of the European Union Member States

2020 ◽  
pp. 97-105
Author(s):  
Aleksandra Kusztykiewicz-Fedurek
Keyword(s):  
European Union ◽  
Negative Impact ◽  
The European Union ◽  
Member States ◽  
Eu Member States ◽  
Political Security ◽  
New Institutions ◽  
The Stability ◽  
Key Aspects ◽  
The Eu

Political security is very often considered through the prism of individual states. In the scholar literature in-depth analyses of this kind of security are rarely encountered in the context of international entities that these countries integrate. The purpose of this article is to draw attention to key aspects of political security in the European Union (EU) Member States. The EU as a supranational organisation, gathering Member States first, ensures the stability of the EU as a whole, and secondly, it ensures that Member States respect common values and principles. Additionally, the EU institutions focus on ensuring the proper functioning of the Eurozone (also called officially “euro area” in EU regulations). Actions that may have a negative impact on the level of the EU’s political security include the boycott of establishing new institutions conducive to the peaceful coexistence and development of states. These threats seem to have a significant impact on the situation in the EU in the face of the proposed (and not accepted by Member States not belonging to the Eurogroup) Eurozone reforms concerning, inter alia, appointment of the Minister of Economy and Finance and the creation of a new institution - the European Monetary Fund.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

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