Thermodynamics calculator matlab software#
Some available software tools for mathematical analysis of ODE based dynamical models. Furthermore, for use in systems with more than four ODEs, bifurcation and stability analysis is often problematic as finding exact solutions for higher-dimensional systems is non-trivial and often intractable. Whilst often versatile, these tools are difficult for non-specialists to work with and are generally focused on users with some grounding in the mathematics of dynamical systems analysis. There are several tools available for the numerical analysis of dynamical ODEs (See Table 1 for details). However, performing these analyses robustly requires a relatively high degree of competency with mathematical theory of dynamical systems. Methods that include steady-state analysis and basin of attraction characterisation are necessary to understand the stability, resilience and persistence of the modelled microbial populations. Mathematical analysis of such model structures is commonplace in fields such as chemostat theory, predator-prey system analysis, theoretical microbial ecology, and more recently in application to synthetic microbiology. The motif models are developed as systems of Ordinary Differential Equations (ODEs) used to describe the dynamics of and interactions between the individual organisms and their various components.
The software presented here focuses on a mechanistic understanding of microbial interactions and, specifically, their analysis and simulation for two or three microbial species and associated substrates and products. For clarity, we define motif here to be analogous to interaction modules described by population ecologists, and the specific forms of these motifs are described widely in the literature (e.g. Mathematical modelling of ecological interactions is affected by the model objective (e.g., observation, prediction, control), the availability of existing knowledge and data, and the structural complexity necessary to adequately describe the motif. Food-webs, defined as a subset or module of larger, more complex networks, are used to analyse ecological interactions at the community or population level, as first described by mathematicians such as Lotka and Volterra, and have been widely used to explore phenomena observed at both macro- and micro-scales. Network motifs provide an approach to understand and characterise the behaviour of living systems at genomic, metabolic and ecological scales. Affiliation: School of Civil Engineering and Geosciences, Newcastle University, Newcastle-upon-Tyne NE1 7RU, United KingdomĪffiliation: School of Mathematics and Statistics, Newcastle University, Newcastle-upon-Tyne NE1 7RU, United Kingdom