nonlinearities

Nonlinearities refer to situations where the relationship between cause and effect isn't straight or predictable by a simple, direct rule. In a linear system, doubling an input doubles the output—for example, adding more sugar makes a drink sweeter proportionally. In a nonlinear system, small changes in input can cause big, unpredictable, or complex changes in output, like adding a tiny amount of a drug causing a large reaction. Many real-world systems—such as weather, ecosystems, or financial markets—are nonlinear, meaning their behavior can't be accurately described with straight-line assumptions.