Linear Equilibrium

The equilibrium points can be found by equating the term in the right of equation 9.3 to a matrix with zeros in the two lines, giving a

Equilibrium, in physics, the condition of a system when neither its state of motion nor its internal energy state tends to change with time.

In this section we will define equilibrium solutions (or equilibrium points) for autonomous differential equations, y' = f(y).

To find the equilibrium points of a system, simply set all the ODEs in the system equal to zero and solve for the values of the dependent variables that make

In section 19.2, we saw that we could “linearize” a nonlinear system about an equilibrium point, to obtain a linear differential equation which giverns the

In Physics, equilibrium is the state in which all the individual forces (and torques) exerted upon an object are balanced. This principle is applied to the

In mathematics, specifically in differential equations, an equilibrium point is a constant solution to a differential equation.

In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential