相关论文: Exploring the Duffing Equation: Numerical Analysis…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential equations (PDEs) with nonlocal advection are increasingly…
In this paper, we studied phase-space analysis of a certain mathematical model of tumor growth with an immune responses and chemotherapy therapy. Mathematical modelling of this process is viewed as a potentially powerful tool in the…
Sensitivity analysis is an effective tool for systematically identifying specific perturbations in parameters that have significant effects on the behavior of a given biosystem, at the scale investigated. In this work, using a…
Classical approaches to analyzing dynamical systems, including bifurcation analysis, can provide invaluable insights into underlying structure of a mathematical model, and the spectrum of all possible dynamical behaviors. However, these…
Acidosis in tumors arises from reprogrammed metabolism and compromised vasculature, creating a harsh, acidic microenvironment that drives the evolutionary selection of acid-resistant cell phenotypes. A mathematical model is proposed to…
Genomic alterations lead to cancer complexity and form a major hurdle for a comprehensive understanding of the molecular mechanisms underlying oncogenesis. In this review, we describe the recent advances in studying cancer-associated genes…
A mathematical model of genome degradation is proposed that takes into account a variable rate of mutation and increasing number of cells in a developing human organism. The model explains known properties of cancer development, in…
This paper explores how the modelling of energy systems may lead to undue closure of alternatives by generating an excess of certainty around some of the possible policy options. We exemplify the problem with two cases: first, the…
Central to the quest for a deeper understanding of the cancer growth and spread process, the naturally multiscale character of cancer invasion demands appropriate multiscale modelling and analysis approach. The cross-talk between the tissue…
In the end of the second decade of 20th century, Warburg showed how cancer cells present a fermentative respiration process, related to a metabolic injury. Here, we develop an analysis of the cell process based on its heat outflow, in order…
We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a class of dephasing models where the state of the initial environment…
Forest transitions, characterized by dynamic shifts between forest, agricultural, and abandoned lands, are complex phenomena. This study developed a stochastic differential equation model to capture the intricate dynamics of these…
Modern X-ray spectroscopy has proven itself as a robust tool for probing the electronic structure of atoms in complex environments. Despite working on energy scales that are much larger than those corresponding to nuclear motions, taking…
In this paper, dynamical systems theory and bifurcation theory are applied to investi- gate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous…
Nonlocality is important in realistic mathematical models of physical and biological systems when local models fail to capture the essential dynamics and interactions that occur over a range of distances. This review illustrates different…
The sensitivity analysis of biological system models can significantly contribute to identifying and explaining influences of internal or external changes on model and its elements. We propose here a comprehensive framework to study…
The MEK/ERK signalling pathway is involved in cell division, cell specialisation, survival and cell death. Here we study a polynomial dynamical system describing the dynamics of MEK/ERK proposed by Yeung et al. with their experimental…
Extensive systematization of theoretical and experimental nuclear densities and of optical potential strengths exctracted from heavy-ion elastic scattering data analyses at low and intermediate energies are presented.The energy-dependence…