I am trying to find mathematical models used in Biology that uses a system of differential equations.
I found the lotka-volterra model and Michaelis-Menten kinetics but I would like to know more than just this two.
Can anyone give a suggestion?
Thanks
Ironically, it can be hard to find mathematical modelling in biology that is not differential equations. But here are some examples.
The Hodgkin-Huxley model (or other biological neuron models) of the cellular dynamics of neurons. The Hindmarsh-Rose model is another simple model that exhibits bursting.
Mathematical models of oncological tumor growth (e.g. [1] or [2]).
Among predator-prey models, there are quite a few DE models beyond Lotka-Volterra. You can also extend to spatial distributions using PDEs (e.g. [1] or [2]). Fisher's equation is a related model of gene propagation.
Turing's model of developmental morphogenesis (e.g. [1] or [2]).
In pharmacology, you can model ADME kinetics via DEs called PBPK models (e.g. here)
The rate equations play a large role in biochemistry. Of course, this is related to the Michaelis-Menten equation.
The spreading of the electrophysiological cardiac contraction signal is modelled either by a reaction-diffusion or an eikonal equation (e.g. here).
The replicator equation is a common DE in evolutionary game theory.
Non-linear differential equations are good models for cellular dynamics, incorporating gene expression, translation, the cell cycle, etc... (e.g. [1], [2]).
There are large-scale models of neural activity (i.e. modelling neural populations rather than single neurons) that utilize differential equations (e.g. [1], [2]). See also neural mass model.
In the field of animal behaviour, often stochastic differential equations are used (though that is true for many of the other ones mentioned above too). You can, however, look at collective flocking behaviours (e.g. the Cucker-Smale model) and compartmental models of behaviour (described via DEs).
Also pretty much everything in biophysics is described by differential equations (e.g. models of protein folding, molecular dynamics, continuum mechanical modelling of tissue, etc...).
