Phase Plane Analysis of One- And Two-Dimensional Autonomous ODE Systems
Example ODE system 10
Example ODE system 11
Example ODE system 12
Example ODE system 13
Example ODE system 14
Example ODE system 15
Example ODE system 2
Example ODE system 3
Example ODE system 4
Example ODE system 5
Example ODE System 6
Example ODE system 7
Example ODE system 8
The species competition model
A function such that we can apply DRY in param documentation
Stable and unstable manifolds
Example ODE system 1
Example ODE system 9
The exponential growth model
Equilibrium point identification
Flow field
The Lindemann mechanism
The logistic growth model
The Lotka-Volterra model
The monomolecular growth model
The Morris-Lecar model
Nullclines
Numerical solution and plotting
Phase plane analysis
Phase portrait plot
Phase plane analysis of one- and two-dimensional autonomous ODE system...
The simple pendulum model
The SIR epidemic model
Stability analysis
The genetic toggle switch model
Phase plane trajectory plotting
The Van der Pol oscillator
The von Bertalanffy growth model
Performs a qualitative analysis of one- and two-dimensional autonomous ordinary differential equation systems, using phase plane methods. Programs are available to identify and classify equilibrium points, plot the direction field, and plot trajectories for multiple initial conditions. In the one-dimensional case, a program is also available to plot the phase portrait. Whilst in the two-dimensional case, programs are additionally available to plot nullclines and stable/unstable manifolds of saddle points. Many example systems are provided for the user. For further details can be found in Grayling (2014) <doi:10.32614/RJ-2014-023>.