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Need to Obtain Bifurcation Points and Bi...

Tamour_Mahwish 0 Maple 2019
ode differential-equations bifurcation
April 16 2024
0 0

Hello Everyone;

I need to find the bifurcation point and further bifarcation diagram for the given model. But facing error. Can anybody help to do this? Can you refer some library for bifurcation analysis of ODE's? Code is attched. Thanks in Advance. 

123.mw

 

 

 

 

> 

restart

> 

C_m := 1.0; g_K := 36.0; I_inj := 0; g_L := .3; E_Na := 50.0; E_K := -77.0; E_L := -54.4
> 

alpha_m := (.1*(V-25.0))/(1-exp(-(V-25.0)*(1/10))); beta_m := 4*exp(-V/(18.0)); alpha_h := 0.7e-1*exp(-V/(20.0)); beta_h := 1/(1+exp(-(V-30)*(1/10))); alpha_n := (0.1e-1*(V-10.0))/(1-exp(-(V-10.0)/(10.0))); beta_n := .125*exp(-V/(80.0)); I_Na := g_Na*m^3*h*(V-E_Na); I_K := g_K*n^4*(V-E_K); I_L := g_L*(V-E_L)

.125*exp(-0.1250000000e-1*V)

(1.1)
> 

eq1 := (I_inj-I_Na-I_K-I_L)/C_m; m := alpha_m/(alpha_m+beta_m); n := alpha_n/(alpha_n+beta_n); h := alpha_h/(alpha_h+beta_h)

-16.32000000-1.000000000*g_Na*m^3*h*(V-50.0)-36.00000000*n^4*(V+77.0)-.3000000000*V

 

.1*(V-25.0)/((1-exp(-(1/10)*V+2.500000000))*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V)))

 

0.1e-1*(V-10.0)/((1-exp(-.1000000000*V+1.000000000))*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V)))

 

0.7e-1*exp(-0.5000000000e-1*V)/(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3)))

(1.2)
> 

bif_eq1 := eq1 = 0;

-16.32000000-0.7000000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))-0.3600000000e-6*(V-10.0)^4*(V+77.0)/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)-.3000000000*V = 0

> 

bif_eq2 := diff( eq1, V) = 0;

-0.2100000000e-3*g_Na*(V-25.0)^2*exp(-0.5000000000e-1*V)*(V-50.0)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.2100000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)*exp(-(1/10)*V+2.500000000)/((1-exp(-(1/10)*V+2.500000000))^4*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.2100000000e-3*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)*(.1/(1-exp(-(1/10)*V+2.500000000))-0.1000000000e-1*(V-25.0)*exp(-(1/10)*V+2.500000000)/(1-exp(-(1/10)*V+2.500000000))^2-.2222222222*exp(-0.5555555556e-1*V))/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^4*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.3500000000e-5*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.7000000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)*(-0.3500000000e-2*exp(-0.5000000000e-1*V)+(1/10)*exp(-(1/10)*V+3)/(1+exp(-(1/10)*V+3))^2)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3)))^2)-0.7000000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))-0.1440000000e-5*(V-10.0)^3*(V+77.0)/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)+0.1440000000e-6*(V-10.0)^4*(V+77.0)*exp(-.1000000000*V+1.000000000)/((1-exp(-.1000000000*V+1.000000000))^5*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)+0.1440000000e-5*(V-10.0)^4*(V+77.0)*(0.1e-1/(1-exp(-.1000000000*V+1.000000000))-0.1000000000e-2*(V-10.0)*exp(-.1000000000*V+1.000000000)/(1-exp(-.1000000000*V+1.000000000))^2-0.1562500000e-2*exp(-0.1250000000e-1*V))/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^5)-0.3600000000e-6*(V-10.0)^4/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)-.3000000000 = 0

 

 

 
> 

bif_sol := solve({ bif_eq1,bif_eq2}, {V, g_Na});

Warning, solutions may have been lost

 

 

as the solutions, which are then expressed as the points mu, y via

   

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