How to do you appropriately define nested functions and variables within the function defining the differential equations for the ode45 solver?

Hello I'm a graduate student who's relatively new to Matlab. Recently, I've been trying to build an ecological model that numerically evaluates a system of four first-order ode's using the ode45 function. I have done this successfully before, but this time several of the differential equations defined in the function handle of the solver (@odefun) are themselves dependent upon nested step-wise functions. When running the code, I have consistently gotten errors saying that the nested functions are undefined in the function that describes the differentials. To resolve this, I have tried to make all the nested variables global using the global command, but then the output of the function that describes the differentials is a vector of length 0, rather than a vector of length 4 that is required to integrate in the ode45 solver. While I'm probably not describing this right, I believe the problem lies in correctly communicating the output of the nested functions to the outer functions. Any help you can provide would be most appreciated. Thanks in advance. Here is the code I'm using. I apologize if this isn't formatted correctly.

function sealice_v1 ()

T = [0 2000];

F_init = 200000;              
C_init = 0;      
Z_init = 0;      
L_init = 29;     

% Parameters
omega = 6.7;
beta = 1;
sigma =0.15;
m = 0.6;
del = 0.0077;
chi = 0.033;
lambda = 0.08;
V = 8000;
R = 1;
L_max = 148;
tau=0.9;

parameters = [omega beta sigma m del chi lambda V R L_max tau];

[T N] = ode45(@odefun, T, [F_init; C_init; Z_init; L_init], parameters) 
end

function f_prime = odefun(T, N, parameters)

global C F L intensity psi F_prime

F = N(1); 
C = N(2); 
Z = N(3); 
L = N(4);

   function intensityout = intensityfunc ()
          intensityfunc = C ./(F*(0.0006821)*L^3.24)
              function psiout=psifunc ()
                  if intensityfunc >= 0 && intensityfunc <= 0.01 
                      psifunc = 1
                  elseif intensityfunc > 0.01
                      psifunc = 1.05+intensityfunc
                  end 
              end
      end

intensity = intensityout
psi = psiout

      function F_prime_out = F_prime_func ()
                  if intensity >= 0 && intensity <= 0.1;
                  F_prime_func = 0;
                  else
                  F_prime_func = -0.09*F;  
                  end
      end

F_prime = F_prime_out

omega = 6.7; 
beta = 1; 
sigma =0.15; 
m = 0.6; 
del = 0.0077; 
chi = 0.033; 
lambda = 0.08; 
V = 8000;  
R = 1; 
L_max = 148; 
tau=0.9;

C_prime = (1-m)*beta*((F*Z)/V)*(1-(intensity/sigma))-(del*C);
Z_prime = (0.5*R*omega*C)-(beta*((F*Z)/V)*(1-(intensity/sigma)))-(tau*Z)-(chi*Z);
L_prime = (lambda*(L_max-L))./psi; 

f_prime = [F_prime; C_prime; Z_prime; L_prime]

end