This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.
We incorporate logistic growth into the moose dynamics, and we replace the death flow of the moose with a kill rate modeled from the kill rate data found on the Isle Royale website.
Thanks to Jacob Englert for the model if-then-else structure.
I start with these parameters: Wolf Death Rate = 0.15 Wolf Birth Rate = 0.0187963 Moose Birth Rate = 0.4 Carrying Capacity = 2000 Initial Moose: 563 Initial Wolves: 20
I used RK-4 with step-size 0.1, from 1959 for 60 years.
The moose birth flow is logistic, MBR*M*(1-M/K) Moose death flow is Kill Rate (in Moose/Year) Wolf birth flow is WBR*Kill Rate (in Wolves/Year) Wolf death flow is WDR*W
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This insight implements Newton's method as an InsightMaker model.
It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.
This insight implements Newton's method as an InsightMaker model.
It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.
This insight implements Newton's method as an InsightMaker model.
It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.
We incorporate logistic growth into the moose dynamics, and we replace the death flow of the moose with a kill rate modeled from the kill rate data found on the Isle Royale website.
Thanks to Jacob Englert for the model if-then-else structure.
I start with these parameters: Wolf Death Rate = 0.15 Wolf Birth Rate = 0.0187963 Moose Birth Rate = 0.4 Carrying Capacity = 2000 Initial Moose: 563 Initial Wolves: 20
I used RK-4 with step-size 0.1, from 1959 for 60 years.
The moose birth flow is logistic, MBR*M*(1-M/K) Moose death flow is Kill Rate (in Moose/Year) Wolf birth flow is WBR*Kill Rate (in Wolves/Year) Wolf death flow is WDR*W
This insight implements Newton's method as an InsightMaker model.
It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This insight implements Newton's method as an InsightMaker model.
It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.
This insight implements Newton's method as an InsightMaker model.
It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.
This insight implements integration as an InsightMaker model.
It is important to use Euler's method, with Simulation Length equal to n, in Seconds.
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.