Related papers: Mathematical Models for Fish Schooling
The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model…
While a rich variety of self-propelled particle models propose to explain the collective motion of fish and other animals, rigorous statistical comparison between models and data remains a challenge. Plausible models should be flexible…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved…
In this paper, we propose a fractional differential equation of order one-half, to model the evolution through time of the dynamics of accumulation and elimination of the contaminant in human organism with a deficient immune system, during…
Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE model is more…
This article provides a survey on some main results and recent developments in the mathematical theory of water waves. More precisely, we briefly discuss the mathematical modeling of water waves and then we give an overview of local and…
Previous likelihood-based linear modeling of nutritional data has been limited by the availability of software that allows flexible error structures in the data. We demonstrate the use of a Bayesian modeling approach to the analysis of such…
This article reviews the current state of teaching and learning mathematical modeling in the context of sustainable development goals for education at the tertiary level. While ample research on mathematical modeling education and published…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
We guide the reader on a journey through mathematical modeling and numerical analysis, emphasizing the crucial interplay of both disciplines. Targeting undergraduate students with basic knowledge in dynamical systems and numerical methods…
In traditional harvesting model a fishing effort E is defined by the fishing intensity and does not address the inverse effect of fish abundance on the fishing effort. In this paper, based on a canonical differential equation model, we…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
The aim of this chapter is to identify and characterise the pedagogical model prescribed for this particular mathematics teaching delivered in post-primary vocational training. More specifically, the contribution investigates two major…
We study the effect of stochastic feeding costs on animal-based commodities with particular focus on aquaculture. More specifically, we use soybean futures to infer on the stochastic behaviour of salmon feed, which we assume to follow a…
Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
This paper deals with the filtering problem for a class of discrete time stochastic volatility models in which the disturbances have rational probability density functions. This includes the Cauchy distributions and Student t-distributions…
Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in…