Question about the basin of attraction of the origin – math.stackexchange.com

Question about the basin of attraction of the origin – math.stackexchange.com

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Consider the system $$x'=(\epsilon x+2y)(z+1)$$ $$y'=(\epsilon y-x)(z+1)$$ $$z'=-z^3$$ (a) Show that the origin is not asymptotically stable when $\epsilon=0.$ (b) Show that when $\epsilon <0,$ ...

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