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.",
"t": [
0,
0.0195694716,
0.0391389432,
0.0587084149,
0.0782778865,
0.0978473581,
0.1174168297,
0.1369863014,
0.15655577... |
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 switching to language 1 | 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.",
"t": [
0,
0.0195694716,
0.0391389432,
0.0587084149,
0.0782778865,
0.0978473581,
0.1174168297,
0.1369863014,
0.15655577... |
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.",
"t": [
0,
0.0195694716,
0.0391389432,
0.0587084149,
0.0782778865,
0.0978473581,
0.1174168297,
0.1369863014,
0.15655577... |
11 | - x_0^3 | 1 | [
[]
] | [
[
3.4
],
[
1.6
]
] | Naive critical slowing down (statistical mechanics) | x_0: order parameter | strogatz p.41 | [
[
"-x_0**3"
]
] | [
[
{
"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... | |||
12 | c_0 * x_0 - c_1 * x_0^2 | 1 | [
[
1.8,
0.1107
]
] | [
[
11
],
[
1.3
]
] | x_0 > 0 | c_0 > 0, c_1 > 0 | Photons in a laser (simple) | c_0: G * N0 - k, for G: gain coefficient, N0: initial excited atoms, k: loss rate, c_1: alpha * G, for G: gain coefficient, alpha: rate of atoms dropping back to ground state | x_0: number of photons | strogatz p.55 | [
[
"-0.1107*x_0**2 + 1.8*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... |
13 | c_0 * sin(x_0) * (c_1 * cos(x_0) - 1) | 1 | [
[
0.0981,
9.7
]
] | [
[
3.1
],
[
2.4
]
] | c_0 > 0, c_1 > 0 | Overdamped bead on a rotating hoop | c_0: m * g, for m: mass, g: gravitational acceleration, c_1: r * omega^2 / g, for r: radius, omega: angular velocity | x_0: angle | strogatz p.63 | [
[
"0.0981*(9.7*cos(x_0) - 1)*sin(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... | |
14 | c_0 * x_0 * (1 - x_0 / c_1) - c_3 * x_0^2 / (c_2^2 + x_0^2) | 1 | [
[
0.78,
81,
21.2,
0.9
]
] | [
[
2.76
],
[
23.3
]
] | x_0 > 0 | c_0 > 0, c_1 > 0, c_2 > 0, c_3 > 0 | Budworm outbreak model with predation | c_0: growth rate, c_1: carrying capacity, c_2: predation onset, c_3: predation limit | x_0: population | strogatz p.75 | [
[
"-0.9*x_0**2/(x_0**2 + 449.44) + 0.78*x_0*(1 - 0.0123456790123457*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... |
15 | c_0 * x_0 * (1 - x_0 / c_1) - x_0^2 / (1 + x_0^2) | 1 | [
[
0.4,
95
]
] | [
[
44.3
],
[
4.5
]
] | x_0 > 0 | c_0 > 0, c_1 > 0 | Budworm outbreak with predation (dimensionless) | c_0: growth rate (<0.5 for young forest, 1 for mature), c_1: carrying capacity (~300 for young forest) | x_0: population | strogatz p.76 | [
[
"-x_0**2/(x_0**2 + 1) + 0.4*x_0*(1 - 0.0105263157894737*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... |
16 | c_0 * x_0 - c_1 * x_0^3 - c_2 * x_0^5 | 1 | [
[
0.1,
-0.04,
0.001
]
] | [
[
0.94
],
[
1.65
]
] | c_0 > 0 | Landau equation (typical time scale tau = 1) | c_0: small dimensionless parameter, c_1: constant, c_2: constant; c_1 > 0 for supercritical bifurcation; c_1 < 0 and c_2 > 0 for subcritical bifurcation | x_0: order parameter | strogatz p.87 | [
[
"-0.001*x_0**5 + 0.04*x_0**3 + 0.1*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... | |
17 | c_0 * x_0 * (1 - x_0 / c_1) - c_2 | 1 | [
[
0.4,
100,
0.3
]
] | [
[
14.3
],
[
34.2
]
] | x_0 > 0 | c_0 > 0, c_1 > 0, c_2 >= 0 | Logistic equation with harvesting/fishing | c_0: growth rate, c_1: carrying capacity, c_2: harvesting rate | x_0: population | strogatz p.89 | [
[
"0.4*x_0*(1 - 0.01*x_0) - 0.3"
]
] | [
[
{
"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... |
18 | c_0 * x_0 * (1 - x_0 / c_1) - c_2 * x_0 / (c_3 + x_0) | 1 | [
[
0.4,
100,
0.24,
50
]
] | [
[
21.1
],
[
44.1
]
] | x_0 > 0 | c_0 > 0, c_1 > 0, c_2 > 0, c_3 > 0 | Improved logistic equation with harvesting/fishing | c_0: growth rate, c_1: carrying capacity, c_2: harvesting rate, c_3: harvesting onset | x_0: population | strogatz p.90 | [
[
"0.4*x_0*(1 - 0.01*x_0) - 0.24*x_0/(x_0 + 50.0)"
]
] | [
[
{
"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... |
19 | x_0 * (1 - x_0) - c_0 * x_0 / (c_1 + x_0) | 1 | [
[
0.08,
0.8
]
] | [
[
0.13
],
[
0.03
]
] | x_0 > 0 | c_0 > 0, c_1 > 0 | Improved logistic equation with harvesting/fishing (dimensionless) | c_0: harvesting rate, c_1: harvesting onset | x_0: population | strogatz p.90 | [
[
"x_0*(1 - x_0) - 0.08*x_0/(x_0 + 0.8)"
]
] | [
[
{
"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... |
20 | c_0 - c_1 * x_0 + x_0^2 / (1 + x_0^2) | 1 | [
[
0.1,
0.55
]
] | [
[
0.002
],
[
0.25
]
] | x_0 > 0 | c_0 >= 0, c_1 > 0 | Autocatalytic gene switching (dimensionless) | c_0: basal production rate, c_1: degradation rate | x_0: gene product | strogatz p.91 | [
[
"x_0**2/(x_0**2 + 1) - 0.55*x_0 + 0.1"
]
] | [
[
{
"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... |
21 | c_0 - c_1 * x_0 - exp(-x_0) | 1 | [
[
1.2,
0.2
]
] | [
[
0
],
[
0.8
]
] | x_0 >= 0 | c_0 >= 1, c_1 > 0 | Dimensionally reduced SIR infection model for dead people (dimensionless) | c_0: death rate, c_1: unknown parameter group | x_0: dead people | strogatz p.92 | [
[
"-0.2*x_0 + 1.2 - exp(-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... |
22 | c_0 + c_1 * x_0^5 / (c_2 + x_0^5) - c_3 * x_0 | 1 | [
[
1.4,
0.4,
123,
0.89
]
] | [
[
3.1
],
[
6.3
]
] | x_0 > 0 | c_0 > 0, c_1 > 0, c_2 > 0, c_3 > 0 | Hysteretic activation of a protein expression (positive feedback, basal promoter expression) | c_0: basal transcription rate, c_1: maximum transcription rate, c_2: activation coefficient, c_3: decay rate | x_0: protein concentration | strogatz p.93 | [
[
"0.4*x_0**5/(x_0**5 + 123.0) - 0.89*x_0 + 1.4"
]
] | [
[
{
"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... |
23 | c_0 - sin(x_0) | 1 | [
[
0.21
]
] | [
[
-2.74
],
[
1.65
]
] | -pi <= x_0 <= pi | c_0 > 0 | Overdamped pendulum with constant driving torque/fireflies/Josephson junction (dimensionless) | c_0: ratio of driving torque to maximum gravitational torque | x_0: angle | strogatz p.104 | [
[
"0.21 - sin(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... |
24 | x_1 | - c_0 * x_0 | 2 | [
[
2.1
]
] | [
[
0.4,
-0.03
],
[
0,
0.2
]
] | c_0 > 0 | Harmonic oscillator without damping | c_0: spring constant to mass ratio | x_0: position, x_1: velocity | strogatz p.126 | [
[
"x_1",
"-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... | |
25 | x_1 | - c_0 * x_0 - c_1 * x_1 | 2 | [
[
4.5,
0.43
]
] | [
[
0.12,
0.043
],
[
0,
-0.3
]
] | c_0 > 0, c_1 > 0 | Harmonic oscillator with damping | c_0: spring constant to mass ratio, c_1: damping coefficient to mass ratio | x_0: position, x_1: velocity | strogatz p.144 | [
[
"x_1",
"-4.5*x_0 - 0.43*x_1"
]
] | [
[
{
"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... | |
26 | x_0 * (c_0 - x_0 - c_1 * x_1) | x_1 * (c_2 - x_0 - x_1) | 2 | [
[
3,
2,
2
]
] | [
[
5,
4.3
],
[
2.3,
3.6
]
] | x_0 > 0, x_1 > 0 | c_0 > 0, c_1 > 0, c_2 > 0 | Lotka-Volterra competition model (Strogatz version with sheeps and rabbits) | c_0: growth rate of rabbits, c_1: death rate of rabbits due to sheeps, c_2: growth rate of sheeps | x_0: rabbits, x_1: sheeps | strogatz p.157 | [
[
"x_0*(-x_0 - 2.0*x_1 + 3.0)",
"x_1*(-x_0 - x_1 + 2.0)"
]
] | [
[
{
"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... |
27 | x_0 * (c_0 - c_1 * x_1) | - x_1 * (c_2 - c_3 * x_0) | 2 | [
[
1.84,
1.45,
3,
1.62
]
] | [
[
8.3,
3.4
],
[
0.4,
0.65
]
] | x_0 > 0, x_1 > 0 | c_0 > 0, c_1 > 0, c_2 > 0, c_3 > 0 | Lotka-Volterra simple (as on Wikipedia) | c_0: growth rate of prey without predators, c_1: killing rate of prey due to predators, c_2: death rate of predators without prey, c_3: growth rate of predators per prey | x_0: prey, x_1: predators | https://en.wikipedia.org/wiki/Lotka-Volterra_equations | [
[
"x_0*(1.84 - 1.45*x_1)",
"-x_1*(3.0 - 1.62*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... |
28 | x_1 | - c_0 * sin(x_0) | 2 | [
[
0.9
]
] | [
[
-1.9,
0
],
[
0.3,
0.8
]
] | -pi <= x_0 <= pi | c_0 > 0 | Pendulum without friction | c_0: gravitational acceleration to length ratio | x_0: angle, x_1: angular velocity | strogatz p.169 | [
[
"x_1",
"-0.9*sin(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... |
29 | c_0 * x_0 * x_1 | x_1^2 - x_0^2 | 2 | [
[
0.65
]
] | [
[
3.2,
1.4
],
[
1.3,
0.2
]
] | c_0 > 0 | Dipole fixed point | c_0: constant | x_0: x, x_1: y | strogatz p.181 | [
[
"0.65*x_0*x_1",
"-x_0**2 + x_1**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... | |
30 | x_0 * (x_1 - c_0 * x_0 * x_1) | x_1 * (x_0 - c_0 * x_0 * x_1) | 2 | [
[
1.61
]
] | [
[
0.3,
0.04
],
[
0.1,
0.21
]
] | x_0 > 0, x_1 > 0 | c_0 > 0 | RNA molecules catalyzing each others replication | c_0: catalytic rate | x_0: concentration of molecule 1, x_1: concentration of molecule 2 | strogatz p.187 | [
[
"x_0*(-1.61*x_0*x_1 + x_1)",
"x_1*(-1.61*x_0*x_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... |
31 | - c_0 * x_0 * x_1 | c_0 * x_0 * x_1 - c_1 * x_1 | 2 | [
[
0.4,
0.314
]
] | [
[
7.2,
0.98
],
[
20,
12.4
]
] | x_0 > 0, x_1 > 0 | c_0 > 0, c_1 > 0 | SIR infection model only for healthy and sick | c_0: recovery rate, c_1: infection rate | x_0: healthy, x_1: sick | strogatz p.188 | [
[
"-0.4*x_0*x_1",
"0.4*x_0*x_1 - 0.314*x_1"
]
] | [
[
{
"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... |
32 | x_1 | - c_0 * x_1 + x_0 - x_0^3 | 2 | [
[
0.18
]
] | [
[
-1.8,
-1.8
],
[
5.8,
0
]
] | c_0 > 0 | Damped double well oscillator | c_0: damping coefficient | x_0: position, x_1: velocity | strogatz p.190 | [
[
"x_1",
"-x_0**3 + x_0 - 0.18*x_1"
]
] | [
[
{
"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... | |
33 | - sin(x_1) - c_0 * x_0^2 | x_0 - cos(x_1) / x_0 | 2 | [
[
0.08
]
] | [
[
5,
0.7
],
[
9.81,
-0.8
]
] | x_0 > 0 | c_0 > 0 | Glider (dimensionless) | c_0: drag coefficient | x_0: speed, x_1: angle to horizontal | strogatz p.190 | [
[
"-0.08*x_0**2 - sin(x_1)",
"x_0 - cos(x_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... |
34 | x_1 | sin(x_0) * (cos(x_0) - c_0) | 2 | [
[
0.93
]
] | [
[
2.1,
0
],
[
-1.2,
-0.2
]
] | c_0 > 0 | Frictionless bead on a rotating hoop (dimensionless) | c_0: gravitational acceleration over radius times omega^2 | x_0: angle, x_1: angular velocity | strogatz p.191 | [
[
"x_1",
"(cos(x_0) - 0.93)*sin(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... | |
35 | cot(x_1) * cos(x_0) | sin(x_0) * (cos(x_1)^2 + c_0 * sin(x_1)^2) | 2 | [
[
4.2
]
] | [
[
1.13,
-0.3
],
[
2.4,
1.7
]
] | -pi < x_0 <= pi, -pi / 2 <= x_1 <= pi / 2 | c_0 > 0 | Rotational dynamics of an object in a shear flow | c_0: shape dependent parameter | x_0: longitude (angle around z-axis), x_1: latitue (angle from north) | strogatz p.194 | [
[
"cos(x_0)*cot(x_1)",
"(4.2*sin(x_1)**2 + cos(x_1)**2)*sin(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... |
36 | x_1 | - sin(x_0) - x_1 - c_0 * cos(x_0) * x_1 | 2 | [
[
0.07
]
] | [
[
0.45,
0.9
],
[
1.34,
-0.8
]
] | -pi < x_o < pi | c_0 > 0 | Pendulum with non-linear damping, no driving (dimensionless) | c_0: Damping coefficient | x_0: angle, x_1: angular velocity | strogatz p.195 | [
[
"x_1",
"-0.07*x_1*cos(x_0) - x_1 - sin(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... |
37 | x_1 | - x_0 - c_0 * (x_0^2 - 1) * x_1 | 2 | [
[
0.43
]
] | [
[
2.2,
0
],
[
0.1,
3.2
]
] | c_0 > 0 | Van der Pol oscillator (standard form) | c_0: damping parameter for nonlinear damping term | x_0: position, x_1: velocity | strogatz p.200 | [
[
"x_1",
"-x_0 - 0.43*x_1*(x_0**2 - 1)"
]
] | [
[
{
"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... | |
38 | c_0 * (x_1 - x_0^3 / 3 + x_0) | - x_0 / c_0 | 2 | [
[
3.37
]
] | [
[
0.7,
0
],
[
-1.1,
-0.7
]
] | c_0 > 0 | Van der Pol oscillator (simplified form from Strogatz) | c_0: damping parameter for nonlinear damping term | x_0: position, x_1: velocity | strogatz p.214 | [
[
"-1.12333333333333*x_0**3 + 3.37*x_0 + 3.37*x_1",
"-0.29673590504451*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... | |
39 | - x_0 + c_0 * x_1 + x_0^2 * x_1 | c_1 - c_0 * x_0 - x_0^2 * x_1 | 2 | [
[
2.4,
0.07
]
] | [
[
0.4,
0.31
],
[
0.2,
-0.7
]
] | x_0 > 0, x_1 > 0 | c_0 > 0, c_1 > 0 | Glycolytic oscillator, e.g., ADP and F6P in yeast (dimensionless) | c_0: kinetic parameter, c_1: kinetic parameter | x_0: concentration of ADP, x_1: concentration of F6P | strogatz p.207 | [
[
"x_0**2*x_1 - x_0 + 2.4*x_1",
"-x_0**2*x_1 - 2.4*x_0 + 0.07"
]
] | [
[
{
"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... |
40 | x_1 | - x_0 + c_0 * x_1 * (1 - x_0^2) | 2 | [
[
0.886
]
] | [
[
0.63,
-0.03
],
[
0.2,
0.2
]
] | c_0 > 0 | Duffing equation (weakly non-linear oscillation) | c_0: parameter for cubic nonlinearity | x_0: position, x_1: velocity | strogatz p.217 | [
[
"x_1",
"-x_0 + 0.886*x_1*(1 - 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... | |
41 | c_0 * (x_1 - x_0) * (c_1 + x_0^2) - x_0 | c_2 - x_0 | 2 | [
[
15.3,
0.001,
0.3
]
] | [
[
0.8,
0.3
],
[
0.02,
1.2
]
] | x_0 > 0, x_1 > 0 | c_0 > 1, 0 < c_1 < 1, c_2 > 0, 8 * c_0 * c_1 < 1 | Cell cycle model by Tyson for interaction between protein cdc2 and cyclin (dimensionless) | c_0: parameter >> 1, c_1: parameter << 1, c_2: adjustable parameter | x_0: concentration of cdc2, x_1: concentration of cyclin | strogatz p.238 | [
[
"-x_0 + 15.3*(-x_0 + x_1)*(x_0**2 + 0.001)",
"0.3 - 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... |
42 | c_0 - x_0 - c_1 * x_0 * x_1 / (1 + x_0^2) | c_2 * x_0 * (1 - x_1 / (1 + x_0^2)) | 2 | [
[
8.9,
4,
1.4
]
] | [
[
0.2,
0.35
],
[
3,
7.8
]
] | x_0 > 0, x_1 > 0 | c_0 > 0, c_1 > 0, c_2 > 0 | Reduced model for chlorine dioxide-iodine-malonic acid rection (dimensionless) | c_0: empirical rate parameter, c_1: fixed to 4 by strogatz, c_2: empirical rate parameter | x_0: dimensionless I- concentration, x_1: dimensionless ClO2 concentration | strogatz p.260 | [
[
"-4.0*x_0*x_1/(x_0**2 + 1) - x_0 + 8.9",
"1.4*x_0*(-x_1/(x_0**2 + 1) + 1)"
]
] | [
[
{
"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... |
43 | x_1 | c_0 - sin(x_0) - c_1 * x_1 | 2 | [
[
1.67,
0.64
]
] | [
[
1.47,
-0.2
],
[
-1.9,
0.03
]
] | c_0 > 0, c_1 > 0 | Driven pendulum with linear damping / Josephson junction (dimensionless) | c_0: driving force/current, c_1: damping parameter | x_0: angle, x_1: angular velocity | strogatz p.269 | [
[
"x_1",
"-0.64*x_1 - sin(x_0) + 1.67"
]
] | [
[
{
"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... | |
44 | x_1 | c_0 - sin(x_0) - c_1 * x_1 * abs(x_1) | 2 | [
[
1.67,
0.64
]
] | [
[
1.47,
-0.2
],
[
-1.9,
0.03
]
] | c_0 > 0, c_1 > 0 | Driven pendulum with quadratic damping (dimensionless) | c_0: driving torque, c_1: damping parameter | x_0: angle, x_1: angular velocity | strogatz p.300 | [
[
"x_1",
"-0.64*x_1*Abs(x_1) - sin(x_0) + 1.67"
]
] | [
[
{
"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... | |
45 | c_0 * (1 - x_0) - x_0 * x_1^2 | x_0 * x_1^2 - c_1 * x_1 | 2 | [
[
0.5,
0.02
]
] | [
[
1.4,
0.2
],
[
0.32,
0.64
]
] | x_0 > 0, x_1 > 0 | c_0 > 0, c_1 > 0 | Isothermal autocatalytic reaction model by Gray and Scott 1985 (dimensionless) | c_0: rate constant, c_1: rate constant | x_0: concentration 1, x_1: concentration 2 | strogatz p.288 | [
[
"-x_0*x_1**2 - 0.5*x_0 + 0.5",
"x_0*x_1**2 - 0.02*x_1"
]
] | [
[
{
"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... |
46 | c_0 * sin(x_0 - x_1) - sin(x_0) | c_0 * sin(x_1 - x_0) - sin(x_1) | 2 | [
[
0.33
]
] | [
[
0.54,
-0.1
],
[
0.43,
1.21
]
] | c_0 > 0 | Interacting bar magnets | c_0: coupling constant | x_0: angle of magnet 1, x_1: angle of magnet 2 | strogatz p.289 | [
[
"-sin(x_0) + 0.33*sin(x_0 - x_1)",
"-sin(x_1) - 0.33*sin(x_0 - x_1)"
]
] | [
[
{
"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... | |
47 | - x_0 + 1 / (1 + exp(c_0 * x_1 - c_1)) | - x_1 + 1 / (1 + exp(c_0 * x_0 - c_1)) | 2 | [
[
4.89,
1.4
]
] | [
[
0.65,
0.59
],
[
3.2,
10.3
]
] | x_0 > 0, x_1 > 0 | c_0 > 0, c_1 > 0 | Binocular rivalry model (no oscillations) | c_0: strength of mutual antagonism, c_1: strength of input stimulus | x_0: perception of left eye stimulus, x_1: perception of right eye stimulus | strogatz p.290 | [
[
"-x_0 + 1/(0.246596963941606*exp(4.89*x_1) + 1)",
"-x_1 + 1/(0.246596963941606*exp(4.89*x_0) + 1)"
]
] | [
[
{
"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... |
48 | c_0 - x_0 - x_0 * x_1 / (1 + c_1 * x_0^2) | c_2 - x_0 * x_1 / (1 + c_1 * x_0^2) | 2 | [
[
18.3,
0.48,
11.23
]
] | [
[
0.1,
30.4
],
[
13.2,
5.21
]
] | x_0 > 0, x_1 > 0 | c_0 > 0, c_1 > 0, c_2 > 0 | Bacterial respiration model for nutrients and oxygen levels | c_0: parameter, c_1: parameter, c_2: parameter | x_0: concentration of nutrients, x_1: concentration of oxygen | strogatz p.293 | [
[
"-x_0*x_1/(0.48*x_0**2 + 1) - x_0 + 18.3",
"-x_0*x_1/(0.48*x_0**2 + 1) + 11.23"
]
] | [
[
{
"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... |
49 | 1 - (c_0 + 1) * x_0 + c_1 * x_0^2 * x_1 | c_0 * x_0 - c_1 * x_0^2 * x_1 | 2 | [
[
3.03,
3.1
]
] | [
[
0.7,
-1.4
],
[
2.1,
1.3
]
] | x_0 > 0, x_1 > 0 | c_0 > 0, c_1 > 0 | Brusselator: hypothetical chemical oscillation model (dimensionless) | c_0: parameter, c_1: parameter | x_0: concentration of X, x_1: concentration of Y | strogatz p.296 | [
[
"3.1*x_0**2*x_1 - 4.03*x_0 + 1",
"-3.1*x_0**2*x_1 + 3.03*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... |
50 | c_0 - x_0 + x_0^2 * x_1 | c_1 - x_0^2 * x_1 | 2 | [
[
0.24,
1.43
]
] | [
[
0.14,
0.6
],
[
1.5,
0.9
]
] | x_0 > 0, x_1 > 0 | c_0 > 0, c_1 > 0 | Chemical oscillator model by Schnackenberg 1979 (dimensionless) | c_0: parameter, c_1: parameter | x_0: concentration of X, x_1: concentration of Y | strogatz p.296 | [
[
"x_0**2*x_1 - x_0 + 0.24",
"-x_0**2*x_1 + 1.43"
]
] | [
[
{
"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... |
51 | c_0 + sin(x_1) * cos(x_0) | c_1 + sin(x_1) * cos(x_0) | 2 | [
[
1.432,
0.972
]
] | [
[
2.2,
0.67
],
[
0.03,
-0.12
]
] | -pi < x_0 < pi, -pi < x_1 < pi | c_0 > 0, c_1 > 0 | Oscillator death model by Ermentrout and Kopell 1990 | c_0: driving torque 1, c_1: driving torque 2 | x_0: angle 1, x_1: angle 2 | strogatz p.301 | [
[
"sin(x_1)*cos(x_0) + 1.432",
"sin(x_1)*cos(x_0) + 0.972"
]
] | [
[
{
"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... |
52 | c_0 * (x_1 - x_0) | c_1 * (x_0 * x_2 - x_1) | c_2 * (c_3 + 1 - x_2 - c_3 * x_0 * x_1) | 3 | [
[
0.1,
0.21,
0.34,
3.1
]
] | [
[
1.3,
1.1,
0.89
],
[
0.89,
1.3,
1.1
]
] | x_0 > 0, x_1 > 0, x_2 > 0 | c_0 > 0, c_1 > 0, c_2 > 0, c_3 > 0 | Maxwell-Bloch equations (laser dynamics) | c_0: decay rate in cavity, c_1: decay rate atomic polarization, c_2: decay rate population inversion, c_3: pumping energy parameter | x_0: E, x_1: P, x_2: D | strogatz p.82 | [
[
"-0.1*x_0 + 0.1*x_1",
"0.21*x_0*x_2 - 0.21*x_1",
"-1.054*x_0*x_1 - 0.34*x_2 + 1.394"
]
] | [
[
{
"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... |
53 | c_0 - c_5 * x_1 * x_0 / (c_9 + x_0) - c_4 * x_0 | c_1 * x_2 * (c_8 + x_1) - c_2 * x_1 / (c_6 + x_1) - c_3 * x_0 * x_1 / (c_7 + x_1) | - c_1 * x_2 * (c_8 + x_1) + c_2 * x_1 / (c_6 + x_1) + c_3 * x_0 * x_1 / (c_7 + x_1) | 3 | [
[
0.1,
0.6,
0.2,
7.95,
0.05,
0.4,
0.1,
2,
0.1,
0.1
]
] | [
[
0.005,
0.26,
2.15
],
[
0.248,
0.0973,
0.0027
]
] | x_0 > 0, x_1 > 0, x_2 > 0 | c_0 > 0, c_1 > 0, c_2 > 0, c_3 > 0, c_4 > 0, c_5 > 0, c_6 > 0, c_7 > 0, c_8 > 0, c_9 > 0 | Model for apoptosis (cell death) | c_0: parameter, c_1: parameter, c_2: parameter, c_3: parameter, c_4: parameter, c_5: parameter, c_6: parameter, c_7: parameter, c_8: parameter, c_9: parameter | x_0: x, x_1: y, x_2: z | https://epubs.siam.org/doi/10.1137/20M1318043 | [
[
"-0.4*x_0*x_1/(x_0 + 0.1) - 0.05*x_0 + 0.1",
"-7.95*x_0*x_1/(x_1 + 2.0) - 0.2*x_1/(x_1 + 0.1) + 0.6*x_2*(x_1 + 0.1)",
"7.95*x_0*x_1/(x_1 + 2.0) + 0.2*x_1/(x_1 + 0.1) - 0.6*x_2*(x_1 + 0.1)"
]
] | [
[
{
"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... |
54 | c_0 * (x_1 - x_0) | c_1 * x_0 - x_1 - x_0 * x_2 | x_0 * x_1 - c_2 * x_2 | 3 | [
[
5.1,
12,
1.67
]
] | [
[
2.3,
8.1,
12.4
],
[
10,
20,
30
]
] | x_0 > 0, x_1 > 0, x_2 > 0 | c_0 > 0, c_1 > 0, c_2 > 0 | Lorenz equations in well-behaved periodic regime | c_0: Prandtl number (sigma), c_1: Rayleigh number (r), c_2: unnamed parameter (b) | x_0: x, x_1: y, x_2: z | strogatz p.319 | [
[
"-5.1*x_0 + 5.1*x_1",
"-x_0*x_2 + 12.0*x_0 - x_1",
"x_0*x_1 - 1.67*x_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... |
55 | c_0 * (x_1 - x_0) | c_1 * x_0 - x_1 - x_0 * x_2 | x_0 * x_1 - c_2 * x_2 | 3 | [
[
10,
99.96,
2.6666666667
]
] | [
[
2.3,
8.1,
12.4
],
[
10,
20,
30
]
] | x_0 > 0, x_1 > 0, x_2 > 0 | c_0 > 0, c_1 > 0, c_2 > 0 | Lorenz equations in complex periodic regime | c_0: Prandtl number (sigma), c_1: Rayleigh number (r), c_2: unnamed parameter (b) | x_0: x, x_1: y, x_2: z | strogatz p.319 | [
[
"-10.0*x_0 + 10.0*x_1",
"-x_0*x_2 + 99.96*x_0 - x_1",
"x_0*x_1 - 2.66666666666667*x_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... |
56 | c_0 * (x_1 - x_0) | c_1 * x_0 - x_1 - x_0 * x_2 | x_0 * x_1 - c_2 * x_2 | 3 | [
[
10,
28,
2.6666666667
]
] | [
[
2.3,
8.1,
12.4
],
[
10,
20,
30
]
] | x_0 > 0, x_1 > 0, x_2 > 0 | c_0 > 0, c_1 > 0, c_2 > 0 | Lorenz equations standard parameters (chaotic) | c_0: Prandtl number (sigma), c_1: Rayleigh number (r), c_2: unnamed parameter (b) | x_0: x, x_1: y, x_2: z | strogatz p.319 | [
[
"-10.0*x_0 + 10.0*x_1",
"-x_0*x_2 + 28.0*x_0 - x_1",
"x_0*x_1 - 2.66666666666667*x_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... |
57 | c_3 * (- x_1 - x_2) | c_3 * (x_0 + c_0 * x_1) | c_3 * (c_1 + x_2 * (x_0 - c_2)) | 3 | [
[
-0.2,
0.2,
5.7,
5
]
] | [
[
2.3,
1.1,
0.8
],
[
-0.1,
4.1,
-2.1
]
] | c_1 > 0, c_2 > 0 | Rössler attractor (stable fixed point) | c_0: parameter, c_1: parameter, c_2: parameter, c_3: just for time scaling | x_0: x, x_1: y, x_2: z | https://en.wikipedia.org/wiki/Rössler_attractor | [
[
"-5.0*x_1 - 5.0*x_2",
"5.0*x_0 - 1.0*x_1",
"5.0*x_2*(x_0 - 5.7) + 1.0"
]
] | [
[
{
"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... | |
58 | c_3 * (- x_1 - x_2) | c_3 * (x_0 + c_0 * x_1) | c_3 * (c_1 + x_2 * (x_0 - c_2)) | 3 | [
[
0.1,
0.2,
5.7,
5
]
] | [
[
2.3,
1.1,
0.8
],
[
-0.1,
4.1,
-2.1
]
] | c_1 > 0, c_2 > 0 | Rössler attractor (periodic) | c_0: parameter, c_1: parameter, c_2: parameter, c_3: just for time scaling | x_0: x, x_1: y, x_2: z | https://en.wikipedia.org/wiki/Rössler_attractor | [
[
"-5.0*x_1 - 5.0*x_2",
"5.0*x_0 + 0.5*x_1",
"5.0*x_2*(x_0 - 5.7) + 1.0"
]
] | [
[
{
"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... | |
59 | c_3 * (- x_1 - x_2) | c_3 * (x_0 + c_0 * x_1) | c_3 * (c_1 + x_2 * (x_0 - c_2)) | 3 | [
[
0.2,
0.2,
5.7,
5
]
] | [
[
2.3,
1.1,
0.8
],
[
-0.1,
4.1,
-2.1
]
] | c_1 > 0, c_2 > 0 | Rössler attractor (chaotic) | c_0: parameter, c_1: parameter, c_2: parameter, c_3: just for time scaling | x_0: x, x_1: y, x_2: z | https://en.wikipedia.org/wiki/Rössler_attractor | [
[
"-5.0*x_1 - 5.0*x_2",
"5.0*x_0 + 1.0*x_1",
"5.0*x_2*(x_0 - 5.7) + 1.0"
]
] | [
[
{
"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... | |
60 | x_0 * (x_2 - c_1) - c_3 * x_1 | c_3 * x_0 + x_1 * (x_2 - c_1) | c_2 + c_0 * x_2 - x_2^3 / 3. - (x_0^2 + x_1^2) * (1 + c_4 * x_2) + c_5 * x_2 * x_0^3 | 3 | [
[
0.95,
0.7,
0.65,
3.5,
0.25,
0.1
]
] | [
[
0.1,
0.05,
0.05
],
[
-0.3,
0.2,
0.1
]
] | c_0 > 0, c_1 > 0, c_2 > 0, c_3 > 0, c_4 > 0 | Aizawa attractor (chaotic) | c_0: parameter, c_1: parameter, c_2: parameter, c_3: parameter, c_4: parameter | x_0: x, x_1: y, x_2: z | https://analogparadigm.com/downloads/alpaca_17.pdf | [
[
"x_0*(x_2 - 0.7) - 3.5*x_1",
"3.5*x_0 + x_1*(x_2 - 0.7)",
"0.1*x_0**3*x_2 - 0.333333333333333*x_2**3 + 0.95*x_2 - (x_0**2 + x_1**2)*(0.25*x_2 + 1) + 0.65"
]
] | [
[
{
"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... | |
61 | c_0 * x_0 - x_1 * x_2 | c_1 * x_1 + x_0 * x_2 | c_2 * x_2 + x_0 * x_1 / c_3 | 3 | [
[
5,
-10,
-3.8,
3
]
] | [
[
15,
-15,
-15
],
[
8,
14,
-10
]
] | Chen-Lee attractor; system for gyro motion with feedback control of rigid body (chaotic) | c_0: parameter, c_1: parameter, c_2: parameter, c_3: fixed constant; parameters relate to principal moments of inertia | x_0: omega_x, x_1: omega_y, x_2: omega_z; variables are essentially angular velocities | https://doi.org/10.1016/j.chaos.2003.12.034 | [
[
"5.0*x_0 - x_1*x_2",
"x_0*x_2 - 10.0*x_1",
"0.333333333333333*x_0*x_1 - 3.8*x_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... | ||
62 | - x_0 + 1 / (1 + exp(c_0 * x_2 + c_1 * x_1 - c_2)) | c_3 * (x_0 - x_1) | - x_2 + 1 / (1 + exp(c_0 * x_0 + c_1 * x_3 - c_2)) | c_3 * (x_2 - x_3) | 4 | [
[
0.89,
0.4,
1.4,
1
]
] | [
[
2.25,
-0.5,
-1.13,
0.4
],
[
0.342,
-0.431,
-0.86,
0.041
]
] | x_0 > 0, x_1 > 0, x_2 > 0, x_3 > 0 | c_0 > 0, c_1 > 0, c_2 > 0, c_3 > 0 | Binocular rivalry model with adaptation (oscillations) | c_0: strength of mutual antagonism, c_1: influence of adaptation, c_2: strength of input stimulus, c_3: time scale of adaptation | x_0: perception of left eye stimulus, x_1: adaptation of left eye stimulus, x_2: perception of right eye stimulus, x_3: adaptation of right eye stimulus | strogatz p.295 | [
[
"-x_0 + 1/(0.246596963941606*exp(0.4*x_1 + 0.89*x_2) + 1)",
"1.0*x_0 - 1.0*x_1",
"-x_2 + 1/(0.246596963941606*exp(0.89*x_0 + 0.4*x_3) + 1)",
"1.0*x_2 - 1.0*x_3"
]
] | [
[
{
"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... |
63 | - c_1 * x_0 * x_2 | c_1 * x_0 * x_2 - c_0 * x_1 | c_0 * x_1 - c_2 * x_2 | c_2 * x_2 | 4 | [
[
0.47,
0.28,
0.3
]
] | [
[
0.6,
0.3,
0.09,
0.01
],
[
0.4,
0.3,
0.25,
0.05
]
] | 0 < x_0 < 1, 0 < x_1 < 1, 0 < x_2 < 1, 0 < x_3 < 1, x_1 + x_2 + x_3 + x_4 = 1 | c_0 > 0, c_1 > 0, c_2 > 0 | SEIR infection model (proportions) | c_0: transfer rate rate, c_1: transmission rate, c_2: recovery rate | x_0: susceptible, x_1: exposed, x_2: infected, x_3: recovered | https://de.wikipedia.org/wiki/SEIR-Modell | [
[
"-0.28*x_0*x_2",
"0.28*x_0*x_2 - 0.47*x_1",
"0.47*x_1 - 0.3*x_2",
"0.3*x_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... |
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