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I have a system of two recursive equations of which I am trying to explore some basic properties. I would like to look at specific conditions where some inequalities hold but it is tough since they are recursive in nature. For example, here are two equations:

$ Z_t = 1 - \exp\big(-\frac{R_{01} Z_t (1-\alpha) + R_{02}Y_t\alpha}{N}\big) \\ Y_t = 1 - \exp\big(-\frac{R_{02} Y_t (1-\alpha) + R_{01}Z_t\alpha}{N}\big)$

I would like to show under what conditions $Z_t > Y_t$ when $R_{01} < R_{02}$. Any advice on working through this type of problem?

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