Looking to show that (0,0) is a unique fixed point of the following system: $$ \dot{x}=-x-3y^2 \\ \dot{y}=xy-y^3 $$
2026-02-22 19:47:14.1771789634
Finding a unique fixed point for a dynamical system
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You have as equations for stationary points $$ 0=-x-3y^2\\ 0=y(x-y^2). $$ It is easy to see that this has only one solution.