How to analyze and evaluate a system of differential equations without equilibrium points?

There is a system of differential equations containing more than two variables, and the differentials of the variables cannot all be zero at the same time, and the equilibrium point may not exist. Now we can calculate the system to show its phase plane by using Runge-Kutta methods (Ode45 in Matlab). But phase plane is not suitable for analysis and evaluation and there is no quantitative index. Can one give some advice to analyze and evaluate this system? Thank you.

where where c is a constant.

[James Tursa]

This is too broad of a question without knowing what f1 and f2 look like.

[Cola]

@James Tursa Thank you for your reply. I am thinking how to specify the question.

[Star Strider]

Does it have to do with How to pobtain the transfer function in the paper? or something else?

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[John D'Errico]

But you have not even suggested how this is a question about MATLAB.

[Cola]

@Star Strider Thank you sir. The model contains strong nonlinearities so it is difficult to build a transfer function.

[Star Strider]

@Cola — My pleasure. Transfer functions are generally linear by definition, however systems that are nonlinear can be essentially ‘transfer functions’ of a sort if they are linearised models, perhaps with time-varying parameters. (This can get extremely complicated extremely quickly.) They generally use state-space representations rather than typical ‘transfer function’ representations, since those are easier to work with.

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[Cola]

@Star Strider @James Tursa Thank you. I can calculate the system to show its phase plane by using Ode45 in Matlab. I find that the area of the curve around the attractive point maybe a way to evaluate the system of differential equations.

For example. I draw the phase plane by Data.mat as shown below, and (0,20) is the point of attraction.

Now I want to calculate the area as shown below by Data.mat.

The whole area can be divided to these parts.

[Cola]

Let me ask a separate question about calculating the area.