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Diffstat (limited to 'examples')
12 files changed, 46 insertions, 6 deletions
diff --git a/examples/hodgkin_huxley/model.modelica b/examples/hodgkin_huxley_neron_potential/model.modelica index 7e44547..7e44547 100644 --- a/examples/hodgkin_huxley/model.modelica +++ b/examples/hodgkin_huxley_neron_potential/model.modelica diff --git a/examples/hodgkin_huxley/page.md b/examples/hodgkin_huxley_neron_potential/page.md index 4598c97..4598c97 100644 --- a/examples/hodgkin_huxley/page.md +++ b/examples/hodgkin_huxley_neron_potential/page.md diff --git a/examples/lotka_volterra/examples.toml b/examples/lotka_volterra_predator_prey/examples.toml index 0f5fb85..0f5fb85 100644 --- a/examples/lotka_volterra/examples.toml +++ b/examples/lotka_volterra_predator_prey/examples.toml diff --git a/examples/lotka_volterra/model.modelica b/examples/lotka_volterra_predator_prey/model.modelica index 706ebc3..706ebc3 100644 --- a/examples/lotka_volterra/model.modelica +++ b/examples/lotka_volterra_predator_prey/model.modelica diff --git a/examples/lotka_volterra/page.md b/examples/lotka_volterra_predator_prey/page.md index 1ae891d..1ae891d 100644 --- a/examples/lotka_volterra/page.md +++ b/examples/lotka_volterra_predator_prey/page.md diff --git a/examples/van_der_pol/examples.toml b/examples/van_der_pol/examples.toml deleted file mode 100644 index e69de29..0000000 --- a/examples/van_der_pol/examples.toml +++ /dev/null diff --git a/examples/van_der_pol/page.md b/examples/van_der_pol/page.md deleted file mode 100644 index e69de29..0000000 --- a/examples/van_der_pol/page.md +++ /dev/null diff --git a/examples/van_der_pol/model.modelica b/examples/van_der_pol_oscillator/model.modelica index c1aa99b..c1aa99b 100644 --- a/examples/van_der_pol/model.modelica +++ b/examples/van_der_pol_oscillator/model.modelica diff --git a/examples/van_der_pol_oscillator/page.md b/examples/van_der_pol_oscillator/page.md new file mode 100644 index 0000000..ff24c7c --- /dev/null +++ b/examples/van_der_pol_oscillator/page.md @@ -0,0 +1,22 @@ + +The Van der Pol oscillator was originally proposed by the Dutch electrical +engineer and physicist Balthasar van der Pol while he was working at +Philips. Van der Pol found stable oscillations, which he subsequently +called relaxation-oscillations and are now known as a type of limit cycle in +electrical circuits employing vacuum tubes. When these circuits were driven +near the limit cycle, they become entrained, i.e. the driving signal pulls the +current along with it. Van der Pol and his colleague, van der Mark, reported in +the September 1927 issue of Nature that at certain drive frequencies an +irregular noise was deterministic chaos. + +The Van der Pol equation has a long history of being used in both the physical +and biological sciences. For instance, in biology, Fitzhugh and Nagumo +extended the equation in a planar field as a model for action potentials of +neurons. The equation has also been utilised in seismology to model the two +plates in a geological fault, and in studies of phonation to model the right +and left vocal fold oscillators. + +## References + +* Wikipedia: + [Van der Pol oscillator](https://en.wikipedia.org/wiki/Van_der_Pol_oscillator) diff --git a/examples/von_bertalanffy/page.md b/examples/von_bertalanffy/page.md deleted file mode 100644 index ea6e9f1..0000000 --- a/examples/von_bertalanffy/page.md +++ /dev/null @@ -1,5 +0,0 @@ - - -An alternative/solve variant is: - - l = L * (1 - e^(-K * t)) diff --git a/examples/von_bertalanffy/model.modelica b/examples/von_bertalanffy_organism_growth/model.modelica index 4eb45f6..afc6f7f 100644 --- a/examples/von_bertalanffy/model.modelica +++ b/examples/von_bertalanffy_organism_growth/model.modelica @@ -1,6 +1,7 @@ model VonBertalanffyGrowth + "Rate-of-growth model for biological organisms" parameter Real K "growth rate"; - parameter Real L "asymptotic final size"; + parameter Real L "asymptotic final length (L infinity)"; Real l "length"; equation der(l) = K * (L - l); diff --git a/examples/von_bertalanffy_organism_growth/page.md b/examples/von_bertalanffy_organism_growth/page.md new file mode 100644 index 0000000..79a643f --- /dev/null +++ b/examples/von_bertalanffy_organism_growth/page.md @@ -0,0 +1,22 @@ + +The Bertalanffy equation is an equation that describes the rate of growth of a +biological organism. The equation was offered by Ludwig von Bertalanffy in 1969. + +## Solution + +Integrating the equation gives: + + $$ l = L \(1 - e^{-Kt}\) $$ + +## References + +The body of this page comes from Wikipedia. + +* Wikipedia: + [Bertalanffy equation](https://en.wikipedia.org/wiki/Ludwig_von_Bertalanffy#Bertalanffy_equation) +* [The von Bertalanffy growth equation](http://www.pisces-conservation.com/growthhelp/index.html?von_bertalanffy.htm) + +### Papers + +Bertalanffy, L. von, (1969). *General System Theory*. New York: George +Braziller, pp. 136 |