Results 51 to 60 of about 2,529,562 (187)

On the analyzing of bifurcation properties of the one‐dimensional Mackey–Glass model by using a generalized approach

Mathematical Methods in the Applied Sciences, EarlyView.
The goal of this work is to look at how a nonlinear model describes hematopoiesis and its complexities utilizing commonly used techniques with historical and material links. Based on time delay, the Mackey–Glass model is explored in two instances. To offer a range, the relevance of the parameter impacting stability (bifurcation) is recorded.
Shuai Zhang, Yaya Wang, Hongyin Geng, Wei Gao, Esin Ilhan, Haci Mehmet Baskonus   +5 more
wiley   +1 more source

Advanced Fractional Reaction-Diffusion Modeling for Spatio-Temporal Dynamics of Poliovirus Transmission with Disability Outcomes and Vaccination Impacts

European Journal of Pure and Applied Mathematics
This work presents a novel fractional reaction-diffusion model to analyze the spatio-temporal dynamics of poliovirus transmission. Polio, a highly contagious viral infection that primarily affects children under five and can lead to permanent disability,
Kamel Guedri, Rahat Zarin, Basim M. Makhdoum, Hatoon A. Niyazi   +3 more
semanticscholar   +1 more source

A Geometric Interpretation for the Algebraic Properties of Second‐Order Ordinary Differential Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6912-6917, April 2025.
ABSTRACT Nowadays, a substantial portion of investigations concerning the symmetry analysis of differential equations predominantly adhere to a framework comprising the following key procedures: (i) the derivation of symmetries, (ii) the determination of an optimal system, (iii) the utilization of these symmetries to construct invariants or ...
A. Paliathanasis, S. Moyo, P. G. L. Leach   +2 more
wiley   +1 more source

Estimates of Solutions for Integro‐Differential Equations in Epidemiological Modeling

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Integro‐differential equations (IDE) have been applied in a variety of areas of research, including epidemiology. Recently, IDE systems were applied to study dengue fever transmission dynamics at the population level. In this study, we extend the approach presented in a previous study for describing the epidemiological model of dengue fever ...
A. Domoshnitsky, I. Volinsky, S. Biton, V. Steindorf   +3 more
wiley   +1 more source

Non-classical symmetries and the singular manifold method: A further two examples

, 1998
This paper discusses two equations with the conditional Painleve property. The usefulness of the singular manifold method as a tool for determining the non-classical symmetries that reduce the equations to ordinary differential equations with the ...
Ablowitz M J, Ames W F, Bluman G W, Clarkson P A, Clarkson P A, Estévez P G, Estévez P G, Levi D, Olver P J, Olver P J, P G Estévez, P R Gordoa, Painlevé P, Tanriver U, Weiss J, Weiss J, Weiss J   +16 more
core   +1 more source

Integrating factors for second order ODEs [PDF]

Journal of Symbolic Computation, V. 27, No. 5, pp. 501-519 (1999), 2000
A systematic algorithm for building integrating factors of the form mu(x,y), mu(x,y') or mu(y,y') for second order ODEs is presented. The algorithm can determine the existence and explicit form of the integrating factors themselves without solving any differential equations, except for a linear ODE in one subcase of the mu(x,y) problem.
arxiv  

Stable blowup for focusing semilinear wave equations in all dimensions [PDF]

arXiv, 2023
We consider the wave equation with focusing power nonlinearity. The associated ODE in time gives rise to a self-similar solution known as the ODE blowup. We prove the nonlinear asymptotic stability of this blowup mechanism outside of radial symmetry in all space dimensions and for all superlinear powers.
arxiv  

Disease Transmission on Random Graphs Using Edge‐Based Percolation

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Edge‐based percolation methods can be used to analyze disease transmission on complex social networks. This allows us to include complex social heterogeneity in our models while maintaining tractability. Here, we begin by reviewing the seminal works on this field in previous studies by Newman et al. (2002, 2003) and Miller et al. (2012).
Sicheng Zhao, Felicia Maria G. Magpantay
wiley   +1 more source

DelayDiffEq: Generating Delay Differential Equation Solvers via Recursive Embedding of Ordinary Differential Equation Solvers [PDF]

arXiv, 2022
Traditional solvers for delay differential equations (DDEs) are designed around only a single method and do not effectively use the infrastructure of their more-developed ordinary differential equation (ODE) counterparts. In this work we present DelayDiffEq, a Julia package for numerically solving delay differential equations (DDEs) which leverages the
arxiv  

Regimes and Mechanisms of Inflammation Described by a Reaction–Diffusion System

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Inflammation is a biological response of the immune system to external stimuli such as injury or infection. It plays an important role in various diseases including atherosclerosis, cancer, and neurodegenerative diseases. This work presents a generic inflammation model based on reaction–diffusion equations that describes the concentrations of ...
W. El Hajj, N. El Khatib, V. Volpert
wiley   +1 more source