Certainly, there are Matlab codes available to study the oscillatory behavior of differential equations, including neutral differential equations. Here is a very basic example of an Euler method to solve a simple neutral differential equation:

function y = NeutralDiffEqn(N)

% Parameters

h = 0.01; % step size

x = (0:h:N); % Calculates upto y(3)

y = zeros(1,length(x));

y(1) = 1; % initial condition

% Euler method

for i=1:(length(x)-1)

y(i+1) = y(i) + h*(-0.5*y(i-1) + x(i)); % replace with your equation here

end

% Plot

plot(x,y)

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Certainly, there are Matlab codes available to study the oscillatory behavior of differential equations, including neutral differential equations. Here is a very basic example of an Euler method to solve a simple neutral differential equation:

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function y = NeutralDiffEqn(N)

% Parameters

h = 0.01; % step size

x = (0:h:N); % Calculates upto y(3)

y = zeros(1,length(x));

y(1) = 1; % initial condition

% Euler method

for i=1:(length(x)-1)

y(i+1) = y(i) + h*(-0.5*y(i-1) + x(i)); % replace with your equation here

end

% Plot

plot(x,y)

This Matlab script approximates the solution of a neutral differential equation using the Euler method. You can replace the equation in the Euler method with your specific neutral differential equation.

Please note that neutral differential equations can be more complex than regular differential equations and they often require more sophisticated numerical methods or analytical techniques to solve them. The Euler method may not be the best choice for these equations due to its simplicity and the associated numerical errors, but it gives a basic understanding of how you could proceed.

MATLAB codes for analyzing the oscillatory behavior of neutral differential equations are many. One popular tool for this purpose is the MATLAB package DDE-BIFTOOL, which is a collection of MATLAB routines for the numerical analysis of bifurcations of delay differential equations (DDEs).

DDE-BIFTOOL provides a set of powerful and user-friendly tools for the analysis of oscillatory behavior in neutral DDEs. It includes functions for computing the stability and bifurcation properties of periodic orbits, as well as for detecting Hopf bifurcations and their associated periodic orbits.

To get started with DDE-BIFTOOL, you can download it from its official website (http://www.dde-biftool.org/) and follow the installation instructions provided there. Once you have installed the package, you can use its functions to analyze the oscillatory behavior of your neutral DDEs.

Alternatively, you can also find other MATLAB codes for analyzing the oscillatory behavior of neutral DDEs by searching on MATLAB Central (https://www.mathworks.com/matlabcentral/), which is a repository of user-contributed MATLAB code.

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https://www.sciencedirect.com/science/article/abs/pii/S0960077907002172