Non-Linear Systems of ODEs
6.0 Concept
Consider the system of ODEs in 4.0,
$ \frac{dx_1}{dt}=f_1(t,x_1,x_2,...x_n) $
$ \frac{dx_2}{dt}=f_2(t,x_1,x_2,...x_n) $
...
$ \frac{dx_n}{dt}=f_n(t,x_1,x_2,...x_n) $
When the $ n $ ODEs are not all linear, this is a nonlinear system of ODE. Consider an example,
$ \frac{dx}{dt}=x(1-2x-3y) $,
$ \frac{dy}{dt}=2y(3-x-2y) $.
In this tutorial, we will analyse this system in different aspects to build up a basic completed concept.
6.1 Equilibrium Point
An equilibrium point is a constant solution to a differential equation. Hence, for an ODE system, an equilibrium point is going to be a solution of a pair of constants. Set all of the differential terms equal to $ 0 $ to find the equilibrium point.
6.2 Non-Linear Non-Autonomous System
6.3 Exercises
6.4 References
Institute of Natural and Mathematical Science, Massey University. (2017). 160.204 Differential Equations I: Course materials. Auckland, New Zealand.
Robinson, J. C. (2003). An introduction to ordinary differential equations. New York, NY., USA: Cambridge University Press.
