scholarly journals Mathematical analysis of a fractional resource-consumer model with disease developed in consumer

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelheq Mezouaghi ◽  
Abdelkader Benali ◽  
Sunil Kumar ◽  
Salih Djilali ◽  
Anwar Zeb ◽  
...  
Keyword(s):  
Mathematical Analysis ◽  
Numerical Scheme ◽  
Graphical Representation ◽  
Qualitative Investigation ◽  
Consumer Model ◽  
Existence Of Equilibria ◽  
Two Populations ◽  
Theoretical Results ◽  
Resource System ◽  
Consumer Resource

AbstractThe research presents a qualitative investigation of a fractional-order consumer-resource system with the hunting cooperation interaction functional and an infection developed in the resources population. The existence of the equilibria is discussed where there are many scenarios that have been distinguished as the extinction of both populations, the extinction of the infection, the persistence of the infection, and the two populations. The influence of the hunting cooperation interaction functional is also investigated where it can influence the existence of equilibria and their stability. A proper numerical scheme is used for building a proper graphical representation for the goal of confirming the theoretical results.

scholarly journals MODELING FRACTIONAL-ORDER DYNAMICS OF MERS-COV VIA MITTAG-LEFFLER LAW

Fractals ◽  
2021 ◽  
Author(s):  
QU HAIDONG ◽  
MATI UR RAHMAN ◽  
YE WANG ◽  
MUHAMMAD ARFAN ◽  
ADNAN
Keyword(s):  
Numerical Scheme ◽  
Arbitrary Order ◽  
Graphical Representation ◽  
Fixed Point Theory ◽  
Middle Eastern ◽  
Point Theory ◽  
Natural Order ◽  
Comparative Result ◽  
Existence Of A Solution ◽  
Theoretical Results

This paper considers an arbitrary-order mathematical model that analyzes the syndrome type Middle Eastern Coronavirus (MERS-CoV) under the nonsingular Mittag-Leffler derivative. Such types of viruses were transferred from camels to the population of humans in the Arabian deserts. We investigate the said problem for theoretical results and determine the existence of a solution by using the fixed point theory concept. For the approximate solution, the well-known method of iteration arbitrary-order Adams–Bashforth (AB) technique has been used. A numerical scheme is developed for the analyzed problem in the continuation of simulations at different noninteger and natural order for the interval ([Formula: see text]]. The graphical representation shows that all classes show convergence and achieve a stable position with growing time. A good comparative result has been given by the analysis of various noninteger orders with natural orders and achieves stability quickly at fewer non-integer orders.

Phase shift of solitary wave in a one-dimensional granular chain

2019 ◽  
Vol 33 (10) ◽  
pp. 1950085
Author(s):  
Xian-Qing Yang ◽  
Yao Yang ◽  
Yang Jiao ◽  
Wei Zhang
Keyword(s):  
Phase Shift ◽  
Solitary Wave ◽  
Numerical Scheme ◽  
Binary Collision ◽  
One Dimensional ◽  
Binary Collision Approximation ◽  
Fifth Order ◽  
The Waves ◽  
Theoretical Results ◽  
Collision Approximation

In this paper, both the fifth-order Runge–Kutta numerical scheme and binary collision approximation are used to study the phase shift. Both numerical and theoretical results are shown that the solitary wave after head-on collision propagates along the chain behind the reference wave in both even and odd numbers of grain chains. It is the well-known feature of the appearance of the phase shift. Those results are in agreement with the experimental results. Furthermore, it is found that the phase shift is not only related to the collision position of the waves, but also to the position where the time is measured. The value of phase shift increases nonmonotonously with increasing the velocity of the opposite propagation of the wave. Binary collision approximation is applied to analyze the phase shift, and it is found that theoretical results agree well with numerical results, especially in the case of phase shift in odd chain.

scholarly journals A new study for the global asymptotic stability of a general predator-prey model

2021 ◽  
Author(s):  
Manh Tuan Hoang
Keyword(s):  
Asymptotic Stability ◽  
Functional Response ◽  
Mathematical Analysis ◽  
Global Asymptotic Stability ◽  
Lyapunov Stability Theory ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Theoretical Results

In a previous paper [L. M. Ladino, E. I. Sabogal, Jose C. Valverde, General functional response and recruitment in a predator-prey system with capture on both species, Math. Methods Appl. Sci. 38(2015) 2876-2887], a mathematical model for a predator-prey model with general functional response and recruitment including capture on both species was formulated and analyzed. However, the global asymptotic stability (GAS) of this model was only partially resolved. In the present paper, we provide a rigorously mathematical analysis for the complete GAS of the predator-prey model. By using the Lyapunov stability theory in combination with some nonstandard techniques of mathematical analysis for dynamical systems, the GAS of equilibria of the model is determined fully. The obtained results not only provide an important improvement for the population dynamics of the predator-prey model but also can be extended to study its modified versions in the context of fractional-order derivatives. The theoretical results are supported and illustrated by a set of numerical examples.

scholarly journals Geometrical Model of Spiking and Bursting Neuron on a Mug-Shaped Branched Manifold

2020 ◽  
Vol 30 (15) ◽  
pp. 2030044
Author(s):  
Mohamed Gheouali ◽  
Tounsia Benzekri ◽  
René Lozi ◽  
Guanrong Chen
Keyword(s):  
Mathematical Analysis ◽  
Phenomenological Model ◽  
Geometrical Model ◽  
Dynamic Motion ◽  
Bursting Neuron ◽  
Theoretical Results ◽  
Rigorous Mathematical Analysis

Based on the Hodgkin–Huxley and Hindmarsh–Rose models, this paper proposes a geometric phenomenological model of bursting neuron in its simplest form, describing the dynamic motion on a mug-shaped branched manifold, which is a cylinder tied to a ribbon. Rigorous mathematical analysis is performed on the nature of the bursting neuron solutions: the number of spikes in a burst, the periodicity or chaoticity of the bursts, etc. The model is then generalized to obtain mixing burst of any number of spikes. Finally, an example is presented to verify the theoretical results.

scholarly journals Deficiencias en el trazado de gráficas de funciones en estudiantes de bachillerato

2014 ◽  
Vol 8 (2) ◽  
pp. 61-73
Author(s):  
Matías Arce ◽  
Tomás Ortega
Keyword(s):  
High School ◽  
High School Students ◽  
Mathematical Analysis ◽  
Graphical Representation ◽  
Graphical Representations ◽  
School Students ◽  
Cognitive Difficulties ◽  
Concept Of Function

Este trabajo trata sobre el concepto de función, básico en el Análisis Matemático, y, en particular, su representación gráfica. Nos centramos en aspectos relacionados con la forma; es decir, el trazado de dicha representación. Analizamos las representaciones gráficas de funciones existentes en los cuadernos de matemáticas de estudiantes de varias aulas de 1º de Bachillerato. Encontramos deficiencias en el trazado de gráficas que se repiten en un alto número de estudiantes, relacionadas con los conceptos de función y asíntota, con el uso de las escalas en los ejes del diagrama cartesiano y con las características de algunas funciones. Además, discutimos sobre las limitaciones técnicas y las dificultades didácticas y cognitivas que pueden dar lugar a su aparición y hacemos algunas recomendaciones didácticas al respecto.High school students’ deficiencies in plotting graphs of functionsThis paper deals with the concept of function, basic in mathematical analysis, and, in particular, with its graphical representation. We focus our attention on plotting graphs of functions. We analyzed the graphical representations of functions found in mathematical notebooks of high school students. We encountered several deficiencies related to the concepts of function and asymptote, the use of scales in diagram axes and the characteristics of some functions. Besides, we discuss the technical limitations and the didactic and cognitive difficulties that may promote their emergence, and, make some didactic recommendations for teachers.Handle: http://hdl.handle.net/10481/29576Nº de citas en WOS (2017): 1 (Citas de 2º orden, 0)

scholarly journals Numerical Solution of Stieltjes Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1571
Author(s):  
Francisco J. Fernández ◽  
F. Adrián F. Tojo
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Explicit Solution ◽  
Numerical Scheme ◽  
Linear Ordinary Differential Equation ◽  
Stieltjes Integral ◽  
Novel Method ◽  
Theoretical Results

This work is devoted to the obtaining of a new numerical scheme based on quadrature formulae for the Lebesgue–Stieltjes integral for the approximation of Stieltjes ordinary differential equations. This novel method allows us to numerically approximate models based on Stieltjes ordinary differential equations for which no explicit solution is known. We prove several theoretical results related to the consistency, convergence, and stability of the numerical method. We also obtain the explicit solution of the Stieltjes linear ordinary differential equation and use it to validate the numerical method. Finally, we present some numerical results that we have obtained for a realistic population model based on a Stieltjes differential equation and a system of Stieltjes differential equations with several derivators.

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