From the course: Complete Guide to Differential Equations Foundations for Data Science

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Autonomous systems

Autonomous systems

From the course: Complete Guide to Differential Equations Foundations for Data Science

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Autonomous systems

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- [Instructor] Let's continue on in your non-linear journey by exploring autonomous systems. These systems are going to be their own class where you will learn what it is to be autonomous instead of a typical non-autonomous system. Let's jump in. An autonomous system of non-linear differential equations is when the differential equations don't contain the independent variable, t, in the functions themselves. So note that t represents time. This means the right side of your equation, if it is in standard form, will only have the dependent variables, x and y, present, or if there are other variables present, they wil be there as well. Since these systems don't directly depend on the independent variable, t, for time, it makes the system time and variant since they evolve solely based on the current state of the dependent variables, x and y. Let's take a look at how this type of system is notated. Let's say you have your system, dx/dt = f of x, y, and dy/dt = g of x, y. So here, you have…

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