Given the finite difference equation $x_{n+1}=ax_{n}exp(−x_{n})$ for $x_{n}≥0$, where a is a positive constant, describing the population of a species. I've determined the fixed points to be $x^∗=ln(a),0$. How do I go about determining the values of a that will cause the population to become extinct starting from any initial condition?
2026-04-02 04:30:38.1775104238
Finding the values of a that will cause the population to become extinct
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