Dynamic systems in ecological modeling

Dynamic systems play a vital role in ecological modeling to model absence and presents and interaction of species or interactions between economic systems and ecological systems. An ecological system is generally dynamically complex. When thinking of the simplest case, the predator and prey, it is obvious that the predator population is dependent on the presence of prey and vice versa.

Most ecological models can be formulated as a state space representation with:

Here, x is the derivative of the state of the system x. t is the time, u is the input vector of boundary conditions, and y is the output vector. p is a vector of constants/parameters and function f is the state transition function while g is the observation function, see also (Petzoldt and Rinke 2007). f is written in bold for the reason that it can also be a system of ordinary differential equations. In our love and hate example, this was our function love in combination with the ordinary differential...