cycletocycle

Cycletocycle is a concept in systems theory and dynamical modeling that describes how the outcome of one processing cycle becomes the input or condition for the next. It captures inter-cycle feedback and memory effects that unfold across repeated iterations of a process. The term is used to discuss how cycle-to-cycle dependencies shape overall behavior in cyclic systems.

In discrete-time models, cycletocycle refers to the mapping from the end state of cycle n to the initial state of cycle n+1. This cross-cycle coupling can give rise to complex dynamics such as delayed responses, sustained oscillations, or altered stability, even when each cycle's internal dynamics are simple.

Fields that commonly address cycletocycle include manufacturing and batch processing, ecology and agriculture, fermentation, and energy storage. For example, wear or contamination observed at the end of one production cycle can influence the setup and parameters of the next, while residual nutrients after a season can affect the following crop cycle.

Modeling approaches use state-space representations, transfer mappings, and stability analysis to assess how cycle-to-cycle interactions affect performance. It is related to concepts such as memory in dynamical systems, hysteresis, and feedback control across periods.