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Details for: "lotka volterra"

Name: lotka volterra (Key: DRZGT)
Path: ackrep_data/system_models/lotka_volterra View on GitHub
Type: system_model
Short Description: predator-prey model, used to describe the population dynamics of biological systems
Created: 05.08.2022
Compatible Environment: default_conda_environment (Key: CDAMA)
Source Code [ / ]
from cProfile import label
import numpy as np
import system_model
from scipy.integrate import solve_ivp

from ackrep_core import ResultContainer
from ackrep_core.system_model_management import save_plot_in_dir
import matplotlib.pyplot as plt
import os

# link to documentation with examples:

def simulate():
    simulate the system model with scipy.integrate.solve_ivp

    :return: result of solve_ivp, might contains input function

    model = system_model.Model()

    rhs_xx_pp_symb = model.get_rhs_symbolic()
    print("Computational Equations:\n")
    for i, eq in enumerate(rhs_xx_pp_symb):
        print(f"dot_x{i+1} =", eq)

    rhs = model.get_rhs_func()

    # initial state values
    xx0 = [0.44249296, 4.6280594]

    t_end = 20
    tt = np.linspace(0, t_end, 10000)
    simulation_data = solve_ivp(rhs, (0, t_end), xx0, t_eval=tt)

    print(simulation_data.y[:, -1])

    return simulation_data

def save_plot(simulation_data):
    plot your data and save the plot
    access to data via: simulation_data.t   array of time values
                        simulation_data.y   array of data components
                        simulation_data.uu  array of input values

    :param simulation_data: simulation_data of system_model
    :return: None
    # plot of your data
    plt.plot(simulation_data.t, simulation_data.y[0], label="$x_1$ (prey)")
    plt.plot(simulation_data.t, simulation_data.y[1], label="$x_2$ (predators)")
    plt.xlabel("Time [s]")
    plt.ylabel("Number of Animals")
    plt.title("Lotka-Volterra (Predator-Prey) Dynamics")



def evaluate_simulation(simulation_data):
    assert that the simulation results are as expected

    :param simulation_data: simulation_data of system_model
    expected_final_state = [3.02762979, 0.06256621]

    rc = ResultContainer(score=1.0)
    simulated_final_state = simulation_data.y[:, -1]
    rc.final_state_errors = [
        simulated_final_state[i] - expected_final_state[i] for i in np.arange(0, len(simulated_final_state))
    rc.success = np.allclose(expected_final_state, simulated_final_state, rtol=0, atol=1e-2)

    return rc
import sympy as sp
import symbtools as st
import importlib
import sys, os

# from ipydex import IPS, activate_ips_on_exception

from ackrep_core.system_model_management import GenericModel, import_parameters

# Import parameter_file
params = import_parameters()

# link to documentation with examples:

class Model(GenericModel):
    def initialize(self):
        this function is called by the constructor of GenericModel

        :return: None

        # ---------start of edit section--------------------------------------
        # Define number of inputs -- MODEL DEPENDENT
        self.u_dim = 0

        # Set "sys_dim" to constant value, if system dimension is constant
        self.sys_dim = 2

        # ---------end of edit section----------------------------------------

        # check existence of params file
        self.has_params = True
        self.params = params

    def get_rhs_symbolic(self):
        define symbolic rhs function

        :return: matrix of symbolic rhs-functions
        if self.dxx_dt_symb is not None:
            return self.dxx_dt_symb

        # ---------start of edit section--------------------------------------
        x1, x2 = self.xx_symb  # state components
        a, b, c, d = self.pp_symb  # parameters

        # define symbolic rhs functions
        dx1_dt = a * x1 - b * x1 * x2
        dx2_dt = c * x1 * x2 - d * x2

        # rhs functions matrix
        self.dxx_dt_symb = sp.Matrix([dx1_dt, dx2_dt])
        # ---------end of edit section----------------------------------------

        return self.dxx_dt_symb
import sys
import os
import numpy as np
import sympy as sp

import tabulate as tab

# link to documentation with examples:

# set model name
model_name = "Lotka_Volterra"

# ---------- create symbolic parameters
pp_symb = [a, b, c, d] = sp.symbols("a, b, c, d", real=True)

# set numerical values of auxiliary parameters
# tailing "_nv" stands for "numerical value"
a_nv = 1.3
b_nv = 0.9
c_nv = 0.8
d_nv = 1.8

# list of symbolic parameter functions
# tailing "_sf" stands for "symbolic parameter function"
pp_sf = [a_nv, b_nv, c_nv, d_nv]

# range of parameters
a_range = (0, np.inf)
b_range = (0, np.inf)
c_range = (0, np.inf)
d_range = (0, np.inf)

# list of ranges
pp_range_list = [a_range, b_range, c_range, d_range]

#  ---------- list for substitution
# -- entries are tuples like: (independent symbolic parameter, numerical value)
pp_subs_list = []

# OPTONAL: Dictionary which defines how certain variables shall be written
# in the table - key: Symbolic Variable, Value: LaTeX Representation/Code
# useful for example for complex variables: {Z: r"\underline{Z}"}
latex_names = {a: r"\alpha", b: r"\beta", c: r"\gamma", d: r"\delta"}

# ---------- Define LaTeX table

# Define tabular Header

tabular_header = ["Parameter Name", "Symbol", "Value"]

# Define column text alignments
col_alignment = ["left", "center", "left"]

# Define Entries of all columns before the Symbol-Column
# --- Entries need to be latex code
col_1 = [
    "reproduction rate of prey alone",
    "mortality rate of prey per predator",
    "mortality rate of predators",
    "reproduction rate of predators per prey",

# contains all lists of the columns before the "Symbol" Column
# --- Empty list, if there are no columns before the "Symbol" Column
start_columns_list = [col_1]

# contains all lists of columns after the FIX ENTRIES
# --- Empty list, if there are no columns after the "Value" column
end_columns_list = []

Related Problems:
SINDy for Lotka Volterra Model
Extensive Material:
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