examples: expand on lotke-voltera

2 files changed, 32 insertions, 4 deletions

diff --git a/examples/lotka_volterra/model.modelica b/examples/lotka_volterra/model.modelica
index 1ab761e..706ebc3 100644
--- a/examples/lotka_volterra/model.modelica
+++ b/examples/lotka_volterra/model.modelica
@@ -1,10 +1,11 @@
 model LotkaVolterra
+  "Predator-Prey equations describing population dynamics of two biological species"
   parameter Real    alpha;
   parameter Real    beta;
   parameter Real    delta;
   parameter Real    gamma;
-  Real              x;
-  Real              y;
+  Real              x "population of prey";
+  Real              y "population of predator";
 equation
   der(x) = (alpha * x) - (beta * x * y);
   der(y) = (delta * x * y) - (gamma * y);
diff --git a/examples/lotka_volterra/page.md b/examples/lotka_volterra/page.md
index 8b85919..1ae891d 100644
--- a/examples/lotka_volterra/page.md
+++ b/examples/lotka_volterra/page.md
@@ -1,8 +1,35 @@
 
-This is a wikipage!
+The Lotka–Volterra equations, also known as the predator–prey equations, are a
+pair of first-order, [non-linear](https://en.wikipedia.org/wiki/Non-linear),
+differential equations frequently used to describe the dynamics of biological
+systems in which two species interact, one as a predator and the other as prey.
+
+The Lotka–Volterra system of equations is an example of a Kolmogorov
+model, which is a more general framework that can model the dynamics of
+ecological systems with predator-prey interactions, competition, disease, and
+mutualism.
+
+## Solutions to the equations
+
+The equations have periodic solutions and do not have a simple expression in
+terms of the usual trigonometric functions, although they are quite
+tractable.
+
+If none of the non-negative parameters α,β,γ,δ vanishes, three can be absorbed
+into the normalization of variables to leave but merely one behind: Since the
+first equation is homogeneous in x, and the second one in y, the parameters β/α
+and δ/γ, are absorbable in the normalizations of y and x, respectively, and γ
+into the normalization of t, so that only α/γ remains arbitrary. It is the only
+parameter affecting the nature of the solutions.
+
+A linearization of the equations yields a solution similar to simple harmonic
+motion with the population of predators trailing that of prey by 90° in the
+cycle.
 
 ## References
 
+Body text taken from Wikipedia.
+
 * [Mathworld](http://mathworld.wolfram.com/Lotka-VolterraEquations.html)
 * [Wikipedia](https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations)
-
+* [Population dynamics of fisheries](https://en.wikipedia.org/wiki/Population_dynamics_of_fisheries)