# How many solutions to the system of non-linear equations?

So $X(t)$ is a matrix at time $t$ and its elements are $x_{i,j}(t)$, and $\Delta_{i,j}(t)$ is the sum of elements adjacent to $x_{i,j}(t)$.

One time-step forward is defined by the following rule: $$x_{i,j}(t+1) = \frac{x_{i,j}(t)}{1+ \left( x_{i,j}(t) + \Delta_{i,j}(t) \right)^4};$$

If one is given initial conditions $X(t)$ then it is a straightforward procedure to calculate $X(t+1)$ (simply by using the defined rule). But what about calculating $X(t)$ when $X(t+1)$ is given? I'd like to have a firm confirmation that generally these are multiple solutions (unless $X(t+1)$ is trivial, I'm thinking about zero-matrix).

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