Using the logistic map for a PRNG comes with certain limitations:
Periodicity: The logistic map can exhibit periodic behavior for certain parameter values, leading to predictable sequences. This can be addressed by carefully selecting the parameter "r" to ensure chaotic behavior.
Seed Sensitivity: The logistic map is highly sensitive to initial conditions, which can pose challenges in generating truly random numbers. Implementing a robust seed generation mechanism and incorporating external entropy sources can mitigate this issue.
Complexity: The logistic map algorithm may be computationally intensive, especially for FPGA implementations. Simplifying the algorithm or optimizing the hardware design can help address this complexity.
Statistical Properties: While the logistic map can produce chaotic sequences, ensuring that the generated numbers exhibit desired statistical properties like uniform distribution or specific correlation structures may require additional post-processing or modifications to the algorithm.