id int64 1 63 | eq stringlengths 7 217 | dim int64 1 4 | consts listlengths 1 1 | init listlengths 2 2 | init_constraints stringclasses 12
values | const_constraints stringlengths 0 88 | eq_description stringlengths 18 93 | const_description stringlengths 0 174 | var_description stringlengths 10 152 | source stringlengths 13 54 | substituted listlengths 1 1 | solutions listlengths 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | (c_0 - x_0 / c_1) / c_2 | 1 | [
[
0.7,
1.2,
2.31
]
] | [
[
10
],
[
3.54
]
] | x_0 > 0 | c_1 > 0, c_2 > 0 | RC-circuit (charging capacitor) | c_0: fixed voltage source, c_1: capacitance, c_2: resistance | x_0: charge | strogatz p.20 | [
[
"0.303030303030303 - 0.360750360750361*x_0"
]
] | [
[
{
"success": true,
"message": "The solver successfully reached the end of the integration interval.",
"t": [
0,
0.0195694716,
0.0391389432,
0.0587084149,
0.0782778865,
0.0978473581,
0.1174168297,
0.1369863014,
0.15655577... |
2 | c_0 * x_0 | 1 | [
[
0.23
]
] | [
[
4.78
],
[
0.87
]
] | x_0 > 0 | Population growth (naive) | c_0: growth rate | x_0: population | strogatz p.22 | [
[
"0.23*x_0"
]
] | [
[
{
"success": true,
"message": "The solver successfully reached the end of the integration interval.",
"t": [
0,
0.0195694716,
0.0391389432,
0.0587084149,
0.0782778865,
0.0978473581,
0.1174168297,
0.1369863014,
0.15655577... | |
3 | c_0 * x_0 * (1 - x_0 / c_1) | 1 | [
[
0.79,
74.3
]
] | [
[
7.3
],
[
21
]
] | x_0 > 0 | c_1 > 0 | Population growth with carrying capacity | c_0: growth rate, c_1: carrying capacity | x_0: population | strogatz p.22 | [
[
"0.79*x_0*(1 - 0.0134589502018843*x_0)"
]
] | [
[
{
"success": true,
"message": "The solver successfully reached the end of the integration interval.",
"t": [
0,
0.0195694716,
0.0391389432,
0.0587084149,
0.0782778865,
0.0978473581,
0.1174168297,
0.1369863014,
0.15655577... |
4 | 1 / (1 + exp(c_0 - x_0 / c_1)) - 0.5 | 1 | [
[
0.5,
0.96
]
] | [
[
0.8
],
[
0.02
]
] | x_0 > 0 | c_1 > 0 | RC-circuit with non-linear resistor (charging capacitor) | c_0: fixed voltage source, c_1: capacitance | x_0: charge | strogatz p.38 | [
[
"-0.5 + 1/(1 + 1.64872127070013*exp(-1.04166666666667*x_0))"
]
] | [
[
{
"success": true,
"message": "The solver successfully reached the end of the integration interval.",
"t": [
0,
0.0195694716,
0.0391389432,
0.0587084149,
0.0782778865,
0.0978473581,
0.1174168297,
0.1369863014,
0.15655577... |
5 | c_0 - c_1 * x_0^2 | 1 | [
[
9.81,
0.0021175
]
] | [
[
0.5
],
[
73
]
] | c_0 > 0, c_1 > 0 | Velocity of a falling object with air resistance | c_0: gravitational acceleration, c_1: overall drag for human: 0.5 * C * rho * A / m, with drag coeff C=0.7, air density rho=1.21, cross-sectional area A=0.25, mass m=50 | x_0: velocity | strogatz p.38 | [
[
"9.81 - 0.0021175*x_0**2"
]
] | [
[
{
"success": true,
"message": "The solver successfully reached the end of the integration interval.",
"t": [
0,
0.0195694716,
0.0391389432,
0.0587084149,
0.0782778865,
0.0978473581,
0.1174168297,
0.1369863014,
0.15655577... | |
6 | c_0 * x_0 - c_1 * x_0^2 | 1 | [
[
2.1,
0.5
]
] | [
[
0.13
],
[
2.24
]
] | x_0 > 0 | c_0 > 0, c_1 > 0 | Autocatalysis with one fixed abundant chemical | c_0: concentration of abundant chemical A times the rate constant of A + X -> 2 X, c_1: rate constant of A + X -> 2X | x_0: concentration of chemical X | strogatz p.39 | [
[
"-0.5*x_0**2 + 2.1*x_0"
]
] | [
[
{
"success": true,
"message": "The solver successfully reached the end of the integration interval.",
"t": [
0,
0.0195694716,
0.0391389432,
0.0587084149,
0.0782778865,
0.0978473581,
0.1174168297,
0.1369863014,
0.15655577... |
7 | c_0 * x_0 * log(c_1 * x_0) | 1 | [
[
0.032,
2.29
]
] | [
[
1.73
],
[
9.5
]
] | x_0 > 0 | c_0 > 0, c_1 > 0 | Gompertz law for tumor growth | c_0: growth rate, c_1: tumor carrying capacity | x_0: proportional to number of cells (tumor size) | strogatz p.39 | [
[
"0.032*x_0*log(2.29*x_0)"
]
] | [
[
{
"success": true,
"message": "The solver successfully reached the end of the integration interval.",
"t": [
0,
0.0195694716,
0.0391389432,
0.0587084149,
0.0782778865,
0.0978473581,
0.1174168297,
0.1369863014,
0.15655577... |
8 | c_0 * x_0 * (1 - x_0 / c_1) * (x_0 / c_2 - 1) | 1 | [
[
0.14,
130,
4.4
]
] | [
[
6.123
],
[
2.1
]
] | x_0 > 0 | c_0 > 0, c_1 > 0, c_2 > 0 | Logistic equation with Allee effect | c_0: growth rate, c_1: carrying capacity, c_2: Allee effect parameter | x_0: population | strogatz p.39 | [
[
"0.14*x_0*(1 - 0.00769230769230769*x_0)*(0.227272727272727*x_0 - 1)"
]
] | [[{"success":true,"message":"The solver successfully reached the end of the integration interval.","(...TRUNCATED) |
9 | (1 - x_0) * c_0 - x_0 * c_1 | 1 | [
[
0.32,
0.28
]
] | [
[
0.14
],
[
0.55
]
] | 0 < x_0 < 1 | c_0 >= 0, c_1 >= 0 | Language death model for two languages | "c_0: rate of language 1 speakers switching to language 2, c_1: rate of language 2 speakers switchin(...TRUNCATED) | x_0: proportion of population speaking language 1 | strogatz p.40 | [
[
"0.32 - 0.6*x_0"
]
] | [[{"success":true,"message":"The solver successfully reached the end of the integration interval.","(...TRUNCATED) |
10 | (1 - x_0) * c_0 * x_0^c_1 - x_0 * (1 - c_0) * (1 - x_0)^c_1 | 1 | [
[
0.2,
1.2
]
] | [
[
0.83
],
[
0.34
]
] | 0 < x_0 < 1 | 0 <= c_0 <= 1, c_1 > 1 | Refined language death model for two languages | c_0: perceived status of language 1, c_1: adjustable exponent | x_0: proportion of population speaking language 1 | strogatz p.40 | [
[
"-0.8*x_0*(1 - x_0)**1.2 + 0.2*x_0**1.2*(1 - x_0)"
]
] | [[{"success":true,"message":"The solver successfully reached the end of the integration interval.","(...TRUNCATED) |
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