China
Africa
Explore chapters and articles related to this topic
The Operating Regime Approach to Nonlinear Modelling and Control
Published in Roderick Murray-Smith, Tor Arne Johansen, Multiple Model Approaches to Modelling and Control, 2020
Tor Arne Johansen, Roderick Murray-Smith
The earliest model we have found directly based on local models, is from the field of mathematical biology, and dates back to Kolmogoroff (1936). The model is an alternative to the classical Lotka-Volterra model, and based on a decomposition of the system into different regimes (called zones) with qualitatively different behaviour, see (Johansen 1994c) for a detailed discussion.
Towards a New Continuous Improvement Organization Based on Simulation
Published in Engineering Management Journal, 2022
Rafael Alencar de Paula, Abdallah Ben Mosbah, Yuvin Chinniah, Samuel Bassetto
The authors of this work decided to adapt this specific set of differential equations because of its property to balance the two different populations. As explained in the introduction, Equations (1) and (2) established the first LV model, also known as the predator-prey model. The original model was proposed by Lotka firstly (Lotka, 1920) and after Volterra complemented (Odum & Barrett, 1971). Although it is called Lotka–Volterra equations, it was developed separately by them in the 1920s. Initially, LV wrote the equations to understand the balance between the populations of predators and prey, the competition against she’s in a lake. Murray studied this model in his paper from 1993 (Murray, 1993) and more profoundly in 2002, in his book Mathematical Biology (Murray, 2002).
A model of invasion by bodysnatchers from the far reaches of space
Published in International Journal of Mathematical Education in Science and Technology, 2021
Phase I: Introduce the student to the basic concept of a population or predator-prey model, and suggest some reading from standard mathematical biology texts (e.g. Britton, 2012). This can be accompanied by assigning a writing task (e.g. describe the logistic map) to motivate their reading and get them acclimatised to mathematical writing from the start in their project, and a short programming task to ensure they are acquainted with a suitable language for numerical analysis.Phase II: Select a model and undertake analysis using standard techniques:Analytical results such as equilibria and boundaries of the phase space (Section 3.2).Numerical simulation to calculate the largest Lyapunov exponent and identify attractors, chaos and periodicity (Section 3.3–3.5).Phase III: Extension of the model, for example space or stage-structuring of the populations, or investigating further questions such as those suggested in the exercises section (Sections 3.5, 4 and 6).
Uniqueness result for an age-dependent reaction–diffusion problem
Published in Applicable Analysis, 2021
Vo Anh Khoa, Tran The Hung, Daniel Lesnic
We note that in one spatial dimension, the system (2) was also analyzed in [6] with (‘PDE-model’) or without (‘ODE-model’) diffusion. In that paper, the Mathematical Biology interest was in establishing the positivity of the solution for the ODE-model and studying the traveling wave solution and its spreading for the PDE-model. However, in our paper, we do not address the existence of solution (which indeed we assume), but the equally important uniqueness of solution. For this latter objective, we do not need to assume any sign restriction on the solution and we also consider the semi-linear version of the PDE-model of (1) in any dimension with Dirichlet or nonlinear boundary conditions, as given by (4)–(6) below. Moreover, we consider the backward and ill-posed situation where the initial conditions at t = 0 and a = 0 are not known, but instead, we measure the solution at the later times t = T and , as studied in [7].