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Toy Model 1

Wire Diagram

Equations

\(\begin{equation}\\ \dot{X_1} = \alpha_{11}\left[\frac{\rho_1S + K_M + K_MX_4^2/K_I^2}{S + K_M + K_MX_4^2/K_I^2}\right] + \alpha_{12}\left[\frac{\rho_2X_4 + K_2}{X_4 + K_2}\right] - X_1\\ \dot{X_2} = \alpha_2X_1^2 - X_2\\ \dot{X_3} = \alpha_3X_2^2 - X_3\\ \dot{X_4} = \alpha_4X_3^2 - X_4\\ \end{equation}\)

Architectural Constraints

\(\begin{equation}\\ \rho_1 > 1\\ \rho_2 > 1\\ \end{equation}\)

from dspace.display.UI.interactive_input import InteractiveInput

model_equations = ['X1. = a11*rho1*S*X5^-1 + a11*KM*X5^-1 + a11*KM*X4^2/KI^2*X5^-1 + a12*rho2*X4*X6^-1 + a12*K2*X6^-1 - X1',
                   'X2. = a2*X1^2 - X2',
                   'X3. = a3*X2^2 - X3',
                   'X4. = a4*X3^2 - X4',
                   'X5 = S + KM + KM*X4^2/KI^2',
                   'X6 = X4 + K2']

architectural_constraints = ['rho1 > 1', 'rho2 > 1']

symbols = {'a11':r'\alpha_{11}',
           'a12':r'\alpha_{12}',
           'a2':r'\alpha_2',
           'a3':r'\alpha_3',
           'a4':r'\alpha_4',
           'a5':r'\alpha_5',
           'rho1':r'\rho_1',
           'rho2':r'\rho_2',
           'KM':'K_M',
           'KI':'K_I',
           'K2':'K_2',
           'X1':'X_1',
           'X2':'X_2',
           'X3':'X_3',
           'X4':'X_4',
           'X5':'X_5',
           'X6':'X_6',
           }

toy_model_1=InteractiveInput(name='Toy Model 1',
                             equations=model_equations, 
                             constraints=architectural_constraints,
                             symbols=symbols)

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Jason G. Lomnitz
Savageau Lab
Department of Biomedical Engineering
University of California
Davis, CA 95616
jlomn@ucdavis.edu