The Logistic Difference Equation

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The logistic difference equation (or logistic map) , a nonlinear first-order recurrence relation, is a time-discrete analogue of the logistic differential equation, . Like its continuous counterpart, it can be used to model the growth or decay of a process, population, or financial instrument.

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Depending on the value of the constant , the solution of the difference equation can approach an equilibrium, move periodically through some cycle of values, or behave in a chaotic, unpredictable way.

A visualization of solutions to the logistic difference equation can be obtained using what can be called a "