You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: spm_lorenz_k.m
    path of file: ./repos/bspm/thirdparty/spm8
    
    the code of the file until where you have to start completion: function [f] = spm_lorenz_k(x,v,P)
% Equations of motion for coupled Lorenz attractors
% FORMAT [f] = spm_lorenz_k(x,v,P)
% x - hidden states (3 x N)
% v - exogenous input
% P - parameters
%     P.t = N x 1
%     P.k = 1 x 1

    
function [f] = spm_lorenz_k(x,v,P)
% Equations of motion for coupled Lorenz attractors
% FORMAT [f] = spm_lorenz_k(x,v,P)
% x - hidden states (3 x N)
% v - exogenous input
% P - parameters
%     P.t = N x 1
%     P.k = 1 x 1
%__________________________________________________________________________
 
% take expectations and unpack
%--------------------------------------------------------------------------
X  = mean(x,2);                            % order parameters (mean-field)
N  = size(x,2);                            % number of oscillators
 
% p(1): Prandtl number
% p(2): 8/3
% p(3): Rayleigh number
%--------------------------------------------------------------------------
p  = [10; -8/3; 32];
f  = x;
for i = 1:N
    f(:,i) = [-p(1) p(1) 0; p(3) -1 -x(1,i); x(2,i) 0 p(2)]*x(:,i);
    f(:,i) = (f(:,i) + P.k*X)*exp(P.t(i));
end